更改

事实上，任何其他θ的选择都将具有完全相同的能量，这意味着无质量的 [[Goldstone boson|Nambu–Goldstone]] 玻色子的存在，这种模式在势能的最小值绕圆周运动，这也表明存在拉格朗日方程中原始对称性的一些记忆。

事实上，任何其他θ的选择都将具有完全相同的能量，这意味着无质量的 [[Goldstone boson|Nambu–Goldstone]] 玻色子的存在，这种模式在势能的最小值绕圆周运动，这也表明存在拉格朗日方程中原始对称性的一些记忆。

===Other examples 其他例子===

===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。

* 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。

* 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。

==Spontaneous symmetry breaking in physics 物理学中的自发对称性破缺==

==物理学中的自发对称性破缺==

[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric  "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]

[[File:Spontaneous symmetry breaking (explanatory diagram).png|thumb|right|250px|''Spontaneous symmetry breaking illustrated'': At high energy levels (''left''), the ball settles in the center, and the result is symmetric. At lower energy levels (''right''), the overall "rules" remain symmetric, but the symmetric  "[[sombrero|Sombrero]]" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.|链接=Special:FilePath/Spontaneous_symmetry_breaking_(explanatory_diagram).png]]

===Particle physics 粒子物理===

===粒子物理===

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.

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。<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>

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。<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>

====Chiral symmetry 手性对称性====

====手性对称性====

{{Main article|Chiral symmetry breaking}}

{{Main article|Chiral 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.

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，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。

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====

====希格斯机制====

{{Main article|Higgs mechanism|Yukawa interaction}}

{{Main article|Higgs mechanism|Yukawa interaction}}

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。

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===

===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.

目前已知的不能用自发对称破缺来描述的几个例子包括：物质的拓扑有序相，如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性，然而它们是物质的不同相。与自发对称破缺的情况不同，目前还没有一个描述这种状态的一般框架。<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>

目前已知的不能用自发对称破缺来描述的几个例子包括：物质的拓扑有序相，如分数量子霍尔液体和自旋液体。这些状态并不破坏任何对称性，然而它们是物质的不同相。与自发对称破缺的情况不同，目前还没有一个描述这种状态的一般框架。<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====

====连续对称性====

The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.

The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the [[Curie temperature]] and at {{nowrap|1=''h'' = 0}}, where ''h'' is the external magnetic field. Below the [[Curie temperature]], the energy of the system is invariant under inversion of the magnetization ''m''('''x''') such that {{nowrap|1=''m''('''x''') = −''m''(−'''x''')}}. The symmetry is spontaneously broken as {{nowrap|''h'' → 0}} when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant.

  }}</ref>结果表明，在对称哈密顿量存在的情况下，在无限体积的极限下，系统自发地采用手性构型，即打破镜面对称。

  }}</ref>结果表明，在对称哈密顿量存在的情况下，在无限体积的极限下，系统自发地采用手性构型，即打破镜面对称。

===Dynamical symmetry breaking 动力学对称性破缺===

===动力学对称性破缺===

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]]).

  }}</ref>)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。

  }}</ref>)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 广义描述和技术运用==

==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]].)

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 诺贝尔奖==

==诺贝尔奖==

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<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>。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<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>。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 参见==

==参见==

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{{div col|colwidth=24em}}

* [[Autocatalytic reactions and order creation]]

* [[Autocatalytic reactions and order creation]]