Symmetries, Symmetry Breaking, Gauge Symmetries
Symmetries, Symmetry Breaking, Gauge Symmetries
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对称性、对称性破缺、规范对称性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
F. Strocchi
中科院分区：
文献类型：
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作者：
F. Strocchi
讨论了对称、对称破缺和规范对称的概念，并通过可观测值{\em}和{物理状态}来表示它们的操作意义。对于无限扩展的系统，状态落入物理上不相交的{\em相}，其特征是它们在无限或边界条件下的行为，编码在基态中，这提供了对称破缺的原因，而不与居里原理相矛盾。全局规范对称性，虽然不能被观测到，但却可以通过状态的可探测特性（超选择量子数和准统计量）来显示。局部规范对称在物理状态中也看不到；它们只出现在场代数的非正表示中。它们在拉格朗日水平上的作用仅仅是确保局部高斯定律在物理状态上的有效性，这些定律由产生相应全局规范对称性的电流所服从；它们是规范量子场论最独特的物理性质的原因。局部规范群的拓扑不变量定义了超选择量子数，它解释了真空。
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the $\theta$ vacua.