论文标题
纯理论和空间周期性
Pure gauge theories and spatial periodicity
论文作者
论文摘要
通过标准功能积分处理计算出的热平衡中纯量规理论的性质在数学上与理论的基态特性相同，该理论具有在仪表场上施加的空间周期性边界条件。这种理论的状态在理论中没有类似物的状态，在这种理论中，只有与规格不变的操作员相关的物理可观察物必须是周期性的，而不是量规场本身。这些状态位于不受约束的理论中不存在的拓扑部门中。拓扑之所以出现，是因为功能积分中的边界条件在圆柱体上是不变的，但在不受约束的理论中却不是不变的。
Properties of pure gauge theories in thermal equilibrium as calculated via standard functional integral treatments are mathematically identical to ground state properties of a theory with spatially-periodic boundary conditions imposed on the gauge fields. Such a theory has states that have no analog in a theory in which only physical observables associated with gauge-invariant operators are required to be periodic, rather than the gauge fields themselves; these states are in topological sectors that do not exist in the unconstrained theory. The topology arises because the boundary conditions in the functional integral are gauge invariant on a cylinder but not in the unconstrained theory.
