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： 量子电动力学的时序规范的数学结构在两种不同的形式中被仔细考察，这两种形式分别由Weyl代数的正性或规则性特征所表征。 时间平移不变性与高斯定律约束之间的冲突被证明会导致特殊的特性。 在正性情况下，只有场的指数函数的相关性存在（非规则性），空间平移不是强连续的，因此它们的生成元不存在，出现与自发对称性破缺相关的θ真空简并。 在不定性情况下，谱条件仅在能量正性的意义上成立，可观测量上存在规范不变的θ真空，但无法扩展到场代数上的时间平移不变态，真空在纵向代数上是忠实的，并且出现KMS结构。 在两种情况下都推导出了泛函积分表示，其区别在于实随机场上的遍历测度或复高斯随机场。 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.