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在物理学中，一个作用于系统的（无限）小扰动使系统跨过临界点，通过决定去向分叉的哪个分支来决定系统的命运，这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说，这个选择看起来是任意的。这个过程被称为对称性破缺，因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。

在物理学中，一个作用于系统的（无限）小扰动使系统跨过临界点，通过决定去向分叉的哪个分支来决定系统的命运，这种现象叫做'''<font color="#ff8000">对称性破缺</font>'''。对于一个观测不到扰动(或“噪声”)的外部观察者来说，这个选择看起来是任意的。这个过程被称为对称性破缺，因为这种转变通常使系统从一个对称但无序的状态进入一个或多个确定的状态。在'''<font color="#ff8000">斑图生成</font>'''中对称性破缺起着重要作用。

1972年，诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多即不同》的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>，文中使用对称性破缺的思想表明，即使'''<font color="#ff8000">还原论</font>'''是正确的，但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为，在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。

1972年，诺贝尔奖得主P·W·安德森(P.W.Anderson)在《科学》(Science)杂志上发表了一篇名为《多则异也》（"More is different"）的论文<ref>{{cite journal | last=Anderson | first=P.W. | title=More is Different | journal=Science | volume=177 | issue=4047| pages=393–396 | year=1972 | url=http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf | doi=10.1126/science.177.4047.393 | pmid=17796623 | format=|bibcode = 1972Sci...177..393A }}</ref>，文中使用对称性破缺的思想表明，即使'''<font color="#ff8000">还原论</font>'''是正确的，但它的逆命题'''<font color="#ff8000">建构主义</font>'''是错误的。建构主义认为，在给出描述各组成部分的理论的情况下科学家可以轻易地预测复杂现象。

对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型，二者的区别是，在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。

对称性破缺可以分为'''<font color="#ff8000">显性对称性破缺</font>'''和'''<font color="#ff8000">自发对称性破缺</font>'''两种类型，二者的区别是，在破缺对称性下系统的运动方程是否不变或者基态是否保持不变。

==Examples 例子==

==Examples 例子==

===Sombrero potential===

===Sombrero potential Sombrero势===

Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis.  But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter.  The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref>

Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis.  But the ball may ''spontaneously break'' this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter.  The dome and the ball retain their individual symmetry, but the system does not.<ref>{{cite book |first=Gerald M. |last=Edelman |title=Bright Air, Brilliant Fire: On the Matter of the Mind |location=New York |publisher=BasicBooks |year=1992 |url=https://archive.org/details/brightairbrillia00gera |url-access=registration |page=[https://archive.org/details/brightairbrillia00gera/page/203 203] }}</ref>

[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]

[[Image:Mexican hat potential polar.svg|270px|thumb|left|Graph of Goldstone's "[[sombrero]]" potential function <math>V(\phi)</math>.|链接=Special:FilePath/Mexican_hat_potential_polar.svg]]

In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,

In the simplest idealized relativistic model, the spontaneously broken symmetry is summarized through an illustrative [[scalar field theory]]. The relevant [[Lagrangian (field theory)|Lagrangian]] of a scalar field <math>\phi</math>, which essentially dictates how a system behaves, can be split up into kinetic and potential terms,

在最简单的理想相对论模型中，可以用一个解释性的标量场理论总结自发破对称性。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为，它可以分解成动能项和势能项：

在最简单的理想相对论模型中，可以用一个解释性的标量场理论总结自发对称性破缺。一个标量场 <math>\phi</math>的拉格朗日量从本质上决定了系统的行为，它可以分解成动能项和势能项：

{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}

{{NumBlk|::|<math>\mathcal{L} = \partial^\mu \phi \partial_\mu \phi - V(\phi).</math>|{{EquationRef|1}}}}

for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".

for any real ''θ'' between 0 and 2''π''. The system also has an unstable vacuum state corresponding to {{nowrap|1=''Φ'' = 0}}. This state has a [[Unitary group|U(1)]] symmetry. However, once the system falls into a specific stable vacuum state (amounting to a choice of ''θ''), this symmetry will appear to be lost, or "spontaneously broken".

对于0到2π之间的任何实数θ。系统也有一个不稳定的真空状态，对应于Φ = 0。这个状态具有U(1)对称。然而，一旦系统落入某个稳定真空状态(相当于选择θ)，这种对称性就会消失，或者说“自发破缺”。

其中θ可以取0到2π之间的任何实数。系统也有一个不稳定的真空状态，对应于Φ = 0。这个状态具有U(1)对称。然而，一旦系统落入某个稳定真空状态(相当于选择θ)，这种对称性就会消失，或者说“自发破缺”。

In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.

In fact, any other choice of ''θ'' would have exactly the same energy, implying the existence of a massless [[Goldstone boson|Nambu–Goldstone boson]], the mode running around the circle at the minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian.

===Other examples===

===Other examples 其他例子===

* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.

* For [[ferromagnet]]ic materials, the underlying laws are invariant under spatial rotations. Here, the order parameter is the [[magnetization]], which measures the magnetic dipole density. Above the [[Curie temperature]], the order parameter is zero, which is spatially invariant, and there is no symmetry breaking. Below the Curie temperature, however, the magnetization acquires a constant nonvanishing value, which points in a certain direction (in the idealized situation where we have full equilibrium; otherwise, translational symmetry gets broken as well). The residual rotational symmetries which leave the orientation of this vector invariant remain unbroken, unlike the other rotations which do not and are thus spontaneously broken.

* 对于铁磁性材料，其基本定律在空间旋转下是不变的。在这里，序参量是衡量磁偶极子密度的磁化强度。在居里温度以上，序参量为零，具有空间不变性，不存在对称性破缺。然而，在居里温度以下，磁化强度变成一个恒定的非零值，指向一个特定的方向(在有充分平衡的理想情况下；否则，平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留，而其他旋转对称性自发破缺。

* 对于铁磁性材料，其基本物理定律在空间旋转下是不变的。在这里，序参量是衡量磁偶极子密度的磁化强度。在居里温度以上，序参量为零，具有空间不变性，不存在对称性破缺。然而，在居里温度以下，磁化强度变成一个恒定的非零值，指向一个特定的方向(在有充分平衡的理想情况下；否则，平移对称性也会破缺)。使该向量方向不变的旋转对称性仍然保留，而其他旋转对称性自发破缺。

* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.

* The laws describing a solid are invariant under the full [[Euclidean group]], but the solid itself spontaneously breaks this group down to a [[space group]]. The displacement and the orientation are the order parameters.

* 描述固体的定律在完整的欧几里得群下是不变的，但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。

* 描述固体的物理定律在完整的欧几里得群下是不变的，但固体本身会自发地将这个群分解为一个空间群。其中位移和方向是序参量。

* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.

* General relativity has a Lorentz symmetry, but in [[Friedmann–Lemaître–Robertson–Walker metric|FRW cosmological models]], the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this symmetry. Similar comments can be made about the cosmic microwave background.

* 广义相对论具有洛伦兹对称性，但在FRW宇宙模型中，定义为星系速度的平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场，作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。

* 广义相对论具有洛伦兹对称性，但在FRW宇宙模型中，定义为星系速度平均值(星系在宇宙尺度上的行为就像气体粒子) 的平均 4-速度场，作为序参量会打破这种对称性。对于宇宙微波背景辐射也有类似的评论。

* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.

* For the [[electroweak]] model, as explained earlier, a component of the Higgs field provides the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries suggests why it took so long for us to discover electroweak unification.

* 对于电弱模型，如前面所解释的，希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样，在电弱温度下也有相变。同样的关于我们不倾向于注意破缺对称性的评论，也说明了为什么我们花了这么长时间才发现电弱统一。

* 对于电弱模型，如前面所解释的，希格斯场的一个分量提供了将电弱规范对称性破缺到电磁规范对称性的序参量。和铁磁的例子一样，在电弱温度下也有相变。同样地由于我们不倾向于注意对称性破缺，导致我们花了这么长时间才发现电弱统一。

* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.

* In superconductors, there is a condensed-matter collective field ψ, which acts as the order parameter breaking the electromagnetic gauge symmetry.

* 在超导体中有一个凝聚态集体场ψ，它是打破电磁规范对称性的序参量。

* 在超导体中有一个凝聚态集体场ψ，它是打破电磁规范对称性的序参量。

* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].

* Take a thin cylindrical plastic rod and push both ends together. Before buckling, the system is symmetric under rotation, and so visibly cylindrically symmetric. But after buckling, it looks different, and asymmetric. Nevertheless, features of the cylindrical symmetry are still there: ignoring friction, it would take no force to freely spin the rod around, displacing the ground state in time, and amounting to an oscillation of vanishing frequency, unlike the radial oscillations in the direction of the buckle. This spinning mode is effectively the requisite [[Goldstone boson|Nambu–Goldstone boson]].

* 拿一个细长的圆柱形塑料杆，把两端推到一起。在屈曲之前，系统在旋转下是对称的，因此可见圆柱对称性。但在弯曲之后，它看起来就不同了，而且是不对称的。然而，圆柱对称性的特征仍然存在：忽略摩擦，杆可以不受外力自由地自旋，在时间上取代基态，等于一个频率趋于零的振荡，而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的南部-戈德斯通玻色子。

* 拿一个细长的圆柱形塑料杆，把两端推到一起。在屈曲之前，系统在旋转下是对称的，因此具有圆柱对称性。但在弯曲之后，它看起来就不同了，而且是不对称的。然而，圆柱对称性的特征仍然存在：忽略摩擦，杆可以不受外力自由地自旋，在时间上取代基态，相当于一个频率趋于零的振荡，而不是沿屈曲方向的径向振荡。这种自旋模式实际上是必需的[[Goldstone boson|Nambu–Goldstone]] 玻色子。

* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.

* Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.

* 考虑无限水平面上的一层均匀的流体。这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面，使它变得比上表面热得多。当温度梯度足够大时，就会形成对流单元，打破了欧几里得对称。

* 考虑无限水平面上的一层均匀的流体，这个系统具有欧几里得平面的所有对称性。但是现在均匀地加热底部表面，使它变得比上表面热得多。当温度梯度足够大时，就会形成对流单元，打破了欧几里得对称。

* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.

* Consider a bead on a circular hoop that is rotated about a vertical [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead ends up in one of the two new equilibrium points, thus breaking the symmetry.

* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时，珠子最初会停留在环底部的初始平衡点(直观上稳定，重力势最低)。在一定的临界旋转速度下，这一点将变得不稳定，珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初，系统相对直径是对称的，但在通过临界速度后，珠子最终停留在两个新的平衡点中的一个，从而打破了对称性。

* 考虑一个围绕某个竖直的直径旋转的圆形箍上的珠子。当旋转速度从静止逐渐增加时，珠子最初会停留在环底部的初始平衡点(直观上稳定，重力势最低)。在一定的临界旋转速度下，这一点将变得不稳定，珠子将跳到另外两个新创建的离中心等距离的平衡点中的一个。起初，系统相对直径是对称的，但在通过临界速度后，珠子最终停留在两个新的平衡点中的一个，从而打破了对称性。

In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.

In [[particle physics]], the [[force carrier]] particles are normally specified by field equations with [[gauge symmetry]]; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A ''by the same amount''. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.

An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}

An actual measurement reflects only one solution, representing a breakdown in the symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called [[Spontaneous magnetization|''spontaneous'']] symmetry breaking (SSB) because ''nothing'' (that we know of) breaks the symmetry in the equations.<ref name="Weinberg2011">{{cite book|author=Steven Weinberg|title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature|url=https://books.google.com/books?id=Rsg3PE_9_ccC|date=20 April 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-78786-6}}</ref>{{rp|194–195}}

一个实际的测量只反映了一个解，代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破坏”更好的术语，因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB)，因为(我们所知道的)没有任何东西会打破方程中的对称性。

一个实际的测量只反映了一个解，这代表了其潜在理论的对称性的破缺。在这里“隐藏”是比“破缺”更好的术语，因为对称性总是存在于这些方程中。这种现象被称为自发对称破缺(SSB)，因为(我们所知道的)没有任何东西会打破方程中的对称性。

====Chiral symmetry 手性对称性====

====Chiral symmetry 手性对称性====

Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.

Chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the [[chiral symmetry]] of the [[strong interactions]] in particle physics. It is a property of [[quantum chromodynamics]], the [[quantum field theory]] describing these interactions, and is responsible for the bulk of the mass (over 99%) of the [[nucleons]], and thus of all common matter, as it converts very light bound [[quarks]] into 100 times heavier constituents of [[baryons]]. The approximate [[Nambu–Goldstone boson]]s in this spontaneous symmetry breaking process are the [[pions]], whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking.

手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性，它是核子的大部分质量(超过99%)的成因，因此也是所有普通物质的主要成因，因为它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中，近似的南部-戈德斯通玻色子是介子，其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。

手性对称破缺是粒子物理中影响强相互作用手性对称的自发对称破缺的一个例子。手性对称性破缺是量子色动力学(描述这些相互作用的量子场理论)的一种特性，它是核子的大部分质量(超过99%)的成因，因此也是所有普通物质的主要成因，它将非常轻的束缚夸克转化为100倍重量的重子的成分。在这个自发对称破缺过程中，近似的 [[Nambu–Goldstone boson|Nambu–Goldstone]] 玻色子是介子，其质量比核子的质量轻一个数量级。它是电弱对称破缺的希格斯机制的原型和重要组成部分。

====Higgs mechanism 希格斯机制====

====Higgs mechanism 希格斯机制====

The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.

The strong, weak, and electromagnetic forces can all be understood as arising from [[gauge symmetry|gauge symmetries]]. The [[Higgs mechanism]], the spontaneous symmetry breaking of gauge symmetries, is an important component in understanding the [[superconductivity]] of metals and the origin of particle masses in the standard model of particle physics. One important consequence of the distinction between true symmetries and ''gauge symmetries'', is that the spontaneous breaking of a gauge symmetry does not give rise to characteristic massless Nambu–Goldstone physical modes, but only massive modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics.

强、弱和电磁力都可以理解为来自规范对称。希格斯机制，即规范对称的自发对称破缺机制，是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果，是规范对称性的自发破缺不产生典型的无质量Nambu-Goldstone物理模式，而是只产生有质量的模式，像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。

强、弱和电磁力都可以理解为来自规范对称。希格斯机制，即规范对称的自发对称破缺机制，是理解金属超导性和粒子物理标准模型中粒子质量起源的重要组成部分。区分真正的对称性和规范对称性的一个重要的结果，是规范对称性的自发破缺不产生典型的无质量 Nambu-Goldstone 物理模式，而只产生有质量的模式，像超导体中的等离子体模式,或者粒子物理学中观察到的希格斯模式。

In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.

In the standard model of particle physics, spontaneous symmetry breaking of the {{nowrap|SU(2) × U(1)}} gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The [[W and Z bosons]] are the elementary particles that mediate the [[weak interaction]], while the [[photon]] mediates the [[electromagnetic interaction]]. At energies much greater than 100 GeV, all these particles behave in a similar manner. The [[Unified field theory#Modern progress|Weinberg–Salam theory]] predicts that, at lower energies, this symmetry is broken so that the photon and the massive W and Z bosons emerge.<ref>A Brief History of Time, Stephen Hawking, Bantam; 10th anniversary edition (1998). pp. 73–74.{{ISBN?}}</ref> In addition, fermions develop mass consistently.

在粒子物理的标准模型中，与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量，并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子，而光子介导电磁相互作用。当能量远远大于100 GeV时，所有这些粒子的行为都相似。Weinberg-Salam理论预测，在较低的能量下，这种对称性被打破，光子和大质量的W和Z玻色子就会出现。此外，费米子不断地发展质量。

在粒子物理的标准模型中，与电弱力相关的SU(2) × U(1)规范对称性自发破缺产生多种粒子的质量，并将电磁力和弱相互作用分离。W玻色子和Z玻色子是介导弱相互作用的基本粒子，而光子介导电磁相互作用。当能量远远大于100 GeV时，所有这些粒子的行为都相似。Weinberg-Salam理论预测，在较低的能量下，这种对称性被打破，光子和大质量的W和Z玻色子就会出现。此外，费米子不断地产生质量。

Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.

Without spontaneous symmetry breaking, the [[Standard Model]] of elementary particle interactions requires the existence of a number of particles. However, some particles (the [[W and Z bosons]]) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the [[Higgs mechanism]] to give these particles mass. It also suggests the presence of a new particle, the [[Higgs boson]], detected in 2012.

在没有自发对称性破缺的情况下，基本粒子相互作用的标准模型要求存在多种粒子。然而，一些粒子(W玻色子和Z玻色子)将被预测为无质量的，而实际上它们被观察到有质量。为了克服这个问题，希格斯机制增强了自发对称破缺，从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在，它在2012年被实验探测到。

在没有自发对称性破缺的情况下，基本粒子相互作用的标准模型要求大量粒子的存在。而一些粒子(W玻色子和Z玻色子)会被预测为无质量的，但实际上它们被观察到有质量。为了克服这个问题，希格斯机制增强了自发对称破缺，从而赋予这些粒子质量。它还表明一种新粒子——希格斯玻色子——的存在，它在2012年被实验探测到。

[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.

[[Superconductivity]] of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.

金属的超导性是一种类似于希格斯现象的凝聚态物质，其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称。

金属的超导性是一种类似于希格斯现象的凝聚态物质，其中库珀电子对的凝聚会自发地打破与光和电磁相关的U(1)规范对称性。

===Condensed matter physics 凝聚态物理===

===Condensed matter physics 凝聚态物理===

Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.

Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking [[rotational symmetry]]. In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others.

物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如，晶体是原子的周期性排列，并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极，打破了旋转对称。除了这些例子，还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。

物质的大多数相态都可以通过自发对称性破缺的透镜来理解。例如，晶体是原子的周期性排列，它并非在所有平移下(仅在晶格向量平移的一个小子集下)都是不变的。磁体有朝向特定方向的南极和北极，打破了旋转对称。除了这些例子，还有一大堆其他的物质对称性破缺相——包括液晶的向列相、电荷和自旋密度波、超流体等等。

There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref>

There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as [[Fractional quantum Hall effect|fractional quantum Hall liquids]], and [[Quantum spin liquid|spin-liquids]]. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.<ref name=chen>{{cite journal | last1 = Chen | first1 = Xie | author-link3 = Xiao-Gang Wen | last2 = Gu | first2 = Zheng-Cheng | last3 = Wen | first3 = Xiao-Gang | year = 2010 | title = Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order | journal = Phys. Rev. B | volume = 82 | issue = 15| page = 155138 | doi=10.1103/physrevb.82.155138|arxiv = 1004.3835 |bibcode = 2010PhRvB..82o5138C | s2cid = 14593420 }}</ref>

====Continuous symmetry 连续对称性====

====Continuous symmetry 连续对称性====

Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.

Spontaneous breaking of a continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity.

连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发)南部-戈德斯通模式，它与序参量的缓慢、长波长波动有关。例如，晶体中的振动模式，即声子，与晶体原子的缓慢密度涨落有关。磁铁相关的戈德斯通模式是自旋振荡波，称为自旋波。对于序参量不是守恒量的对称性破缺态，Nambu-Goldstone模通常是无质量的，并以恒定速度传播。

连续对称的自发破缺不可避免地伴随着无间隙(意味着这些模式不需要花费任何能量来激发) [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式，它与序参量的缓慢、长波长波动有关。例如，晶体中的振动模式声子，与晶体原子的缓慢密度涨落有关。磁铁相关的 [[Nambu–Goldstone boson|Goldstone]] 模式是自旋振荡波，称为自旋波。对于序参量不是守恒量的对称性破缺态，Nambu-Goldstone模通常是无质量的，并以恒定速度传播。

An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)

An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.)

由Mermin和Wagner提出的一个重要定理指出，在有限温度下，热激活的南布-戈德斯通模式的扰动破坏了长程有序，并阻止了一维和二维系统中对称性的自发破缺。类似地，即使是在零温度下，序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体，其序参量磁化强度是一个精确的守恒量，不存在任何量子涨落。)

由Mermin和Wagner提出的一个重要定理指出，在有限温度下， [[Nambu–Goldstone boson|Nambu–Goldstone]] 模式热激活的扰动破坏了长程有序，并阻止了一维和二维系统中对称性的自发破缺。类似地，即使是在零温度下，序参量的量子涨落阻止了一维系统中大多数类型的连续对称破缺。(一个重要的例外是铁磁体，其序参量磁化强度是一个精确的守恒量，不存在任何量子涨落。)

Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref>

Other long-range interacting systems, such as cylindrical curved surfaces interacting via the [[Coulomb potential]] or [[Yukawa potential]], have been shown to break translational and rotational symmetries.<ref>

Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).

Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., [[Lagrangian (field theory)|Lagrangian]]).

动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式，在这种情况下，系统的基态比理论描述(例如拉格朗日量)的对称性降低。

动力学对称性破缺(DSB)是自发对称性破缺的一种特殊形式，在这种情况下，系统的基态相对理论描述(例如拉格朗日量)的对称性降低。

Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).

Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the [[effective action]]).

  }}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.

  }}</ref> Dynamical breaking of gauge symmetries is often due to creation of a [[fermionic condensate]] — e.g., the [[quark condensate]], which is connected to the [[Chiral symmetry breaking|dynamical breaking of chiral symmetry]] in [[quantum chromodynamics]]. Conventional [[superconductivity]] is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry.

规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中，存在一个不稳定的希格斯粒子，希格斯粒子驱动真空进入对称破缺相。(例如，参见弱电相互作用。)然而，在规范对称性动力学破缺中，不存在不稳定的希格斯粒子，但系统本身的束缚态提供了导致相变的不稳定场。例如，巴丁、希尔和林德纳发表了一篇论文，试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中，复合粒子扮演希格斯玻色子的角色，通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生，例如夸克凝聚，它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子，声子的吸引导致电子成对结合然后凝聚，从而打破电磁规范对称性。

规范对称性动力学破缺更加微妙。在常规规范对称自发破缺理论中，存在一个不稳定的希格斯粒子，希格斯粒子驱动真空态进入对称破缺相。(例如，参见弱电相互作用。)然而，在规范对称性动力学破缺中，不存在不稳定的希格斯粒子，但系统本身的束缚态提供了导致相变的不稳定场。例如，巴丁、希尔和林德纳发表了一篇论文，试图用一个由顶-反顶夸克束缚状态驱动的DSB来取代标准模型中的传统希格斯机制。(在这种模型中，复合粒子扮演希格斯玻色子的角色，通常被称为“复合希格斯模型”。)规范对称性动力学破缺通常是由于费米凝聚的产生，例如夸克凝聚，它与量子色动力学中手性对称的动力学破缺有关。传统的超导性是凝聚态物质方面的典型例子，声子的吸引导致电子成对结合然后凝聚，从而打破电磁规范对称性。

==Generalisation and technical usage==

==Generalisation and technical usage 广义描述和技术运用==

For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)

For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore [[Symmetry (physics)|symmetric]] with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the [[Nambu–Goldstone boson|Goldstone boson]].)

要发生自发对称性破缺，系统中必须有几个等可能的结果，整个系统相对于这些结果是对称的。然而，如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互)，就必须产生特定的结果。虽然系统作为一个整体是对称的，但它从来没有表现出这种对称性，而只是处于一个特定的不对称状态。于是，在该理论中对称性被自发地打破了。然而，每个结果的可能性都相等这一点，反映了潜在的对称性。因此通常被称为“隐藏对称性”，并具有重要的形式结果。(参见有关戈德斯通玻色子的文章。)

要发生自发对称性破缺，系统中必须有几个等可能的结果，整个系统相对于这些结果是对称的。然而，如果对系统进行采样(即如果系统被实际使用或以任何方式与之交互)，就必须产生特定的结果。虽然系统作为一个整体是对称的，但它从来没有表现出这种对称性，而只是处于一个特定的不对称状态。于是，在该理论中对称性被自发地打破了。然而，每个结果的可能性都相等这一点，反映了潜在的对称性。因此通常被称为“隐藏对称性”，并具有重要的形式结果。(参见有关 [[Nambu–Goldstone boson|Goldstone]]玻色子的文章。)

When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.

When a theory is symmetric with respect to a [[symmetry group]], but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate ''which'' member is distinct, only that ''one is''. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.

The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized  '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.

The crucial concept in physics theories is the [[order parameter]]. If there is a field (often a background field) which acquires an expectation value (not necessarily a [[vacuum expectation value|''vacuum'' expectation value]]) which is not invariant under the symmetry in question, we say that the system is in the [[ordered phase]], and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the [[vacuum state]] does not obey the initial symmetry (which would keep it invariant, in the linearly realized  '''Wigner mode''' in which it would be a singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) '''Nambu–Goldstone mode'''. Normally, in the absence of the Higgs mechanism, massless [[Goldstone boson]]s arise.

在物理理论中，最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值)，这个期望值在理论具有的对称性下不是不变的，我们就说系统处于有序相，对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下，真空状态不服从初始对称性(这将保持它不变，在线性实现的Wigner模式中，它将是一个单线)，而是在(隐藏的)对称下变化，现在在(非线性)南布-戈德斯通模式中实现。通常，在没有希格斯机制的情况下，就会出现无质量的戈德斯通玻色子。

在物理理论中，最重要的概念是序参量。如果有一个场(通常是背景场)得到一个期望值(不一定是真空期望值)，这个期望值在理论具有的对称性下不是不变的，我们就说系统处于有序相，对称性自发破缺。这是因为序参量指定了测量其他子系统与之相互作用的“参考框架”。在这种情况下，真空状态不服从初始对称性(这将保持它不变，在线性实现的Wigner模式中，它将是一个单线)，而是在(隐藏的)对称下变化，现在在(非线性)'''Nambu–Goldstone'''模式中实现。通常，在没有希格斯机制的情况下，就会出现无质量的戈德斯通玻色子。

The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.

The symmetry group can be discrete, such as the [[space group]] of a crystal, or continuous (e.g., a [[Lie group]]), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a [[vacuum state]] of the full [[Quantum mechanics|quantum theory]], although a classical solution may break a continuous symmetry.

对称群可以是离散的，如晶体的空间群，也可以是连续的(如李群)，如空间的旋转对称。然而，如果系统只包含一个空间维度，尽管经典解可能打破连续对称性，那么在全量子理论的真空状态下，只有离散的对称性可能被打破。

对称群可以是离散的，如晶体的空间群，也可以是连续的(如李群)，如空间的旋转对称。然而，如果系统只包含一个空间维度，尽管经典解可能打破连续对称性，那么在全量子理论的真空状态下，只有离散的对称性可能被打破。

==Nobel Prize==

==Nobel Prize 诺贝尔奖==

On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.

On October 7, 2008, the [[Royal Swedish Academy of Sciences]] awarded the 2008 [[Nobel Prize in Physics]] to three scientists for their work in subatomic physics symmetry breaking. [[Yoichiro Nambu]], of the [[University of Chicago]], won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically [[chiral symmetry breaking]]. Physicists [[Makoto Kobayashi (physicist)|Makoto Kobayashi]] and [[Toshihide Maskawa]], of [[Kyoto University]], shared the other half of the prize for discovering the origin of the [[Explicit symmetry breaking|explicit breaking]] of CP symmetry in the weak interactions.<ref>{{cite web|author=The Nobel Foundation|title=The Nobel Prize in Physics 2008|url=http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html|work=nobelprize.org|access-date=January 15, 2008}}</ref> This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon.

2008年10月7日，瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家，以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金，表彰他发现了在强相互作用下对称性自发破缺的机制，特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制，但迄今为止被理解为希格斯耦合的“恰好如此”特征，而不是一种自发的对称破缺现象。

2008年10月7日，瑞典皇家科学院(Royal Swedish Academy of Sciences)将2008年诺贝尔物理学奖授予三位科学家，以表彰他们在亚原子物理对称性破缺方面的工作。芝加哥大学的Yoichiro Nambu获得了一半的奖金，表彰他发现了在强相互作用下对称性自发破缺的机制，特别是手性对称性破缺。京都大学(Kyoto University)物理学家小林诚(Makoto Kobayashi)和正川俊英(Toshihide Maskawa)因发现了弱相互作用中CP对称性显性破缺的起源而分享了另一半奖金。这一起源最终依赖于希格斯机制，但迄今为止被理解为希格斯耦合的“恰好如此”特征，而不是一种自发的对称破缺现象。

==See also==

==See also 参见==

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* [[Autocatalytic reactions and order creation]]

* [[Autocatalytic reactions and order creation]]

[[Category:Quantum phases]]

[[Category:Quantum phases]]

*

 

* 某些结构的随机形成破坏了物理学基本定律的精确对称性；

 

 

 

 

 

 

 

 

 

 

==参考文献==

==参考文献==