更改

[[File:Spontaneous symmetry breaking from an instable equilibrium.svg|thumb|A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.]]

[[File:Spontaneous symmetry breaking from an instable equilibrium.svg|thumb|A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.]]

A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.

A ball is initially located at the top of the central hill (C). This position is an unstable equilibrium: a very small perturbation will cause it to fall to one of the two stable wells left (L) or right (R). Even if the hill is symmetric and there is no reason for the ball to fall on either side, the observed final state is not symmetric.

 

[[图一：一个小球位于中央山丘的山峰处（C）这是一种不稳定的平衡位置，具体表现为:一个很小的扰动会使它下降到稳定井左(L)或右(R)中的一个。即使是对称的,没有理由让球落在两侧,观察到的最终状态是不对称的]]

球最初位于中央山丘的顶部(c)。这个位置是一个不稳定的平衡: 一个非常小的扰动将导致它落到左(l)或右(r)两个稳定的井之一。即使小山是对称的，球没有理由落在任何一边，观察到的最终状态也是不对称的。

 

In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Symmetry breaking is thought to play a major role in pattern formation.

In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Symmetry breaking is thought to play a major role in pattern formation.

在物理学中，对称性破缺是一种现象，在这种现象中，作用于系统的小涨落通过一个临界点决定了系统的命运，通过决定分岔的哪个分支。对于一个不知道波动(或“噪音”)的外部观察者来说，这个选择看起来是随意的。这个过程被称为对称性“破缺” ，因为这种跃迁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。对称性破缺被认为在模式形成中起着重要作用。

在物理学中，对称性破缺是一种现象，在这种现象中，对系统作用一个很小的力使其达到临界点产生波动，从而决定去向分岔的哪个分支。对于一个不知道波动(或“噪音”)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，因为这种跃迁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。在斑图形成中对称性破缺起着重要作用。

In his 1972 Science paper titled "More is different"  Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not.

In his 1972 Science paper titled "More is different"  Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not.

在他1972年发表的题为“更多是不同的”的科学论文中，诺贝尔奖获得者 p.w。用对称性破缺的观点来表明，即使还原论是正确的，其反向的构造论---- 即认为科学家可以轻易地预测复杂现象的理论来描述它们的组成部分---- 也是不正确的。

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《More is different》的论文，文中利用对称性破缺的概念来表明，即使还原论是正确的，但与之相反的建构主义(construcism)却是错误的。建构主义认为，在给出描述其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。

 

Symmetry breaking can be distinguished into two types, explicit symmetry breaking and spontaneous symmetry breaking, characterized by whether the equations of motion fail to be invariant or the ground state fails to be invariant.

Symmetry breaking can be distinguished into two types, explicit symmetry breaking and spontaneous symmetry breaking, characterized by whether the equations of motion fail to be invariant or the ground state fails to be invariant.

 

==Explicit symmetry breaking明显对称性破缺==

==Explicit symmetry breaking==

In explicit symmetry breaking, the equations of motion describing a system are variant under the broken symmetry. In Hamiltonian mechanics or Lagrangian Mechanics, this happens when there is at least one term in the Hamiltonian (or Lagrangian) that explicitly breaks the given symmetry.

In explicit symmetry breaking, the equations of motion describing a system are variant under the broken symmetry. In Hamiltonian mechanics or Lagrangian Mechanics, this happens when there is at least one term in the Hamiltonian (or Lagrangian) that explicitly breaks the given symmetry.

==Spontaneous symmetry breaking==

==Spontaneous symmetry breaking自发对称性破缺==

In spontaneous symmetry breaking, the equations of motion of the system are invariant, but the system is not. This is because the background (spacetime) of the system, its vacuum, is non-invariant. Such a symmetry breaking is parametrized by an order parameter. A special case of this type of symmetry breaking is dynamical symmetry breaking.

In spontaneous symmetry breaking, the equations of motion of the system are invariant, but the system is not. This is because the background (spacetime) of the system, its vacuum, is non-invariant. Such a symmetry breaking is parametrized by an order parameter. A special case of this type of symmetry breaking is dynamical symmetry breaking.

 

== Examples 实例==

== Examples ==

* The breaking of an exact symmetry of the underlying laws of physics by the apparently random formation of some structure;  

* The breaking of an exact symmetry of the underlying laws of physics by the apparently random formation of some structure;  

* 某些结构的明显随机形成破坏了物理学基本定律的精确对称性;

* 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;

:* A situation in physics in which a [[ground state|minimal energy state]] has less symmetry than the system itself;  

:* A situation in physics in which a [[ground state|minimal energy state]] has less symmetry than the system itself;  

* A situation in physics in which a minimal energy state has less symmetry than the system itself;  

* A situation in physics in which a minimal energy state has less symmetry than the system itself;  

* 物理学中的一种情况，即最小能量状态的对称性不如系统本身;

* 物理学中最小能量状态的对称性不如系统本身的一种情况;

:* Situations where the actual state of the system does not reflect the underlying symmetries of the dynamics because the manifestly symmetric state is unstable (stability is gained at the cost of [[local property|local]] asymmetry);  

:* Situations where the actual state of the system does not reflect the underlying symmetries of the dynamics because the manifestly symmetric state is unstable (stability is gained at the cost of [[local property|local]] asymmetry);  

在物理学文献中讨论的首批对称性破缺案例之一，与不可压缩流体在重力和流体静力平衡中的均匀旋转物体的形式有关。在1834年，Jacobi 和后来的 Liouville 讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时，三轴椭球是这个问题的平衡解。在这个分叉点上，麦克劳林椭球体的轴对称性被破坏。此外，在这个分叉点之上，对于常数角动量，使动能最小化的解是非轴对称的 Jacobi 椭球，而不是 Maclaurin 椭球。

在物理学文献中讨论的首批对称性破缺案例之一，与不可压缩流体在重力和流体静力平衡中的均匀旋转物体的形式有关。在1834年，Jacobi 和后来的 Liouville 讨论了这样一个事实: 当旋转物体的动能相对于引力势能超过一定的临界值时，三轴椭球是这个问题的平衡解。在这个分叉点上，麦克劳林椭球体的轴对称性被破坏。此外，在这个分叉点之上，对于常数角动量，使动能最小化的解是非轴对称的 Jacobi 椭球，而不是 Maclaurin 椭球。

 

==See also==

==See also==

*[[1964 PRL symmetry breaking papers]]

*[[1964 PRL symmetry breaking papers]]

==References==

==References==