关于自发对称性破缺理论中真空的对称性
On the symmetry of the vacuum in theories with spontaneous symmetry breaking
摘要：
我们回顾了自发对称性破缺（SSB）现象的通常解释，指出了围绕这个问题的常见误解，特别是在量子场论的背景下。事实上，人们在这方面找到的常见解释表明，在对应于所谓SSB的情况的某些条件下，理论的真空不具有拉格朗日的对称性。我们详细解释了为什么这种说法是不正确的，以及在什么有限的情况下可能出现这种情况。我们集中在全球对称性的情况下，我们发现没有令人满意的论述在现有的文献中，并简要评论的情况下，规范对称性，虽然宣传不够，准确和完整的描述存在。我们简要地讨论了通常归因于自发对称性破缺现象的现象学表现的含义，分析哪些可能受到我们的分析的影响，哪些没有。特别地，我们描述了完全对称方案中的质量生成机制（即，与一个完全对称的真空），并简要讨论了这种分析的影响，在早期宇宙的拓扑缺陷的形成问题。
英文摘要：
We review the usual account of the phenomena of spontaneous symmetry breaking (SSB), pointing out the common misunderstandings surrounding the issue, in particular within the context of quantum field theory. In fact, the common explanations one finds in this context, indicate that under certain conditions corresponding to the situation called SSB, the vacuum of the theory does not share the symmetries of the Lagrangian. We explain in detail why this statement is incorrect in general, and in what limited set of circumstances such situation could arise. We concentrate on the case of global symmetries, for which we found no satisfactory exposition in the existing literature, and briefly comment on the case of gauge symmetries where, although insufficiently publicized, accurate and complete descriptions exist. We briefly discuss the implications for the phenomenological manifestations usually attributed to the phenomena of spontaneous symmetry breaking, analyzing which might be affected by our analysis and which are not. In particular we describe the mass generation mechanism in a fully symmetric scheme (i.e., with a totally symmetric vacuum), and briefly discuss the implications of this analysis to the problem of formation of topological defects in the early universe.
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