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→Generalisation and technical usage
==Generalisation and technical usage==
==Generalisation and technical usage==
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。)
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.
当一个理论相对于一个对称群是对称的，但要求群中的一个元素是不同的，那么就会发生自发对称性破缺。理论不能规定哪个成员是不同的，而只能规定那个成员是不同的。从这一点开始，这个理论就可以被视为这个元素实际上是不同的，附带的条件是，任何以这种方式发现的结果必须是重新对称的，通过取组中每个元素的平均值作为不同的元素。
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。
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。
==Nobel Prize==
==Nobel Prize==