标题： 时间规范的数学结构 显示英文标题

标题： Mathematical structure of the temporal gauge

摘要： 考察了量子电动力学（QED）时间规范的数学结构，该结构在由Weyl代数的正性或正则性特征化的两种替代形式中进行了批判性分析。 展示了时间平移不变性和高斯定律约束之间的冲突导致了特殊特性。 在正性情况下，仅存在场指数的相关性（非正则性），空间平移不是强连续的，因此它们的生成元不存在，出现θ真空退化，这与自发对称破缺相关联。 在不定性情况下，谱条件仅在能量正性的意义上成立，规范不变的θ-真空存在于可观测量上，但在场代数上的时间平移不变状态没有扩展，真空在纵向代数上是忠实的，并且出现了KMS结构。 在两种情况下都推导出了泛函积分表示，其中在实随机场上的遍历测度和复高斯随机场之间存在选择。 显示英文摘要

摘要： The mathematical structure of the temporal gauge of QED is critically examined in both the alternative formulations characterized by either positivity or regularity of the Weyl algebra. The conflict between time translation invariance and Gauss law constraint is shown to lead to peculiar features. In the positive case only the correlations of exponentials of fields exist (non regularity), the space translations are not strongly continuous, so that their generators do not exist, a theta vacuum degeneracy occurs, associated to a spontaneous symmetry breaking. In the indefinite case the spectral condition only holds in terms of positivity of the energy, gauge invariant theta-vacua exist on the observables, with no extension to time translation invariant states on the field algebra, the vacuum is faithful on the longitudinal algebra and a KMS structure emerges. Functional integral representations are derived in both cases, with the alternative between ergodic measures on real random fields or complex Gaussian random fields.