标题： 规范量子化中的QCD θ参数 显示英文标题

标题： The QCD theta-parameter in canonical quantization

摘要： 研究了四维欧几里得环面时空中的纯杨-米尔斯理论中 QCD θ 参数的作用。虽然在这种设定下避免了引入可能的非物理边界条件，但必须明确如何对拓扑扇区求和。为了与实时间可观测量联系起来，我们将配分函数视为正则密度矩阵的迹。系统对应于一个有限温度下的三维空间环面。执行迹运算需要正则量子化和规范固定。固定规范并要求哈密顿量的厄米性得以保持，这限制了物理波泛函的希尔伯特空间，推广了由高斯定律所施加的约束。因此，我们发现，在希尔伯特空间中的态在内积下是适当归一化的，该内积对规范势所表示的每个物理构型积分一次且仅一次。从受限希尔伯特空间导出的可观测量不违反电荷-宇称对称性。我们注意到，对于哈密顿量中任意 θ 值都存在的理论的一个精确隐藏对称性，在这个受限空间中被有效地提升为宇称守恒。这些结果是在为了避免引入边界条件而在环面上推导出来的，当考虑到所有可能的规范变换时，它们也适用于闵可夫斯基时空。 显示英文摘要

摘要： The role of the QCD theta-parameter is investigated in pure Yang-Mills theory in the spacetime given by the four-dimensional Euclidean torus. While in this setting the introduction of possibly unphysical boundary conditions is avoided, it must be specified how the sum over the topological sectors is to be carried out. To connect with observables in real time, we perceive the partition function as the trace over the canonical density matrix. The system then corresponds to one of a finite temperature on a spatial three-torus. Carrying out the trace operation requires canonical quantization and gauge fixing. Fixing the gauge and demanding that the Hermiticity of the Hamiltonian is maintained leads to a restriction of the Hilbert space of physical wave functionals that generalizes the constraints derived from imposing Gauss' law. Consequently, we find that the states in the Hilbert space are properly normalizable under an inner product that integrates over each physical configuration represented by the gauge potential one time and one time only. The observables derived from the constrained Hilbert space do not violate charge-parity symmetry. We note that an exact hidden symmetry of the theory that is present for arbitrary values of theta in the Hamiltonian is effectively promoted to parity conservation in this constrained space. These results, derived on a torus in order to avoid the introduction of boundary conditions, also carry over to Minkowski spacetime when taking account of all possible gauge transformations.