哈密顿形式中的可约规范对称性与非自由规范对称性
Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
摘要：
非自由的规范对称性意味着为规范参数提供的作用泛函零的规范变分受到微分方程的限制。非自由的规范对称性导致了整体守恒量，其壳层上的值由低维曲面上的场或数据的渐近性定义，甚至由时空点上的场或数据的渐近性定义，而不是由柯西超曲面定义.这种量最著名的例子是单模引力的宇宙学常数。文章还提供了更多的例子来说明宇宙学常数的高自旋引力类似物。本文证明了任何具有非自由规范对称性的作用量都具有另一种形式的规范对称性，它具有非限制规范参数的高阶导数。高阶规范对称性一般是可约的，即使非自由对称性不是。详细讨论了约束哈密顿形式中这两种规范对称性之间的关系。证明了从非自由规范代数到可约高阶规范代数的局部映射是存在的，而逆映射一般是非局部的。研究了两种形式的规范对称性的哈密顿BFV-BRST形式。这两个哈密顿形式主义所示连接的正则变换涉及鬼。生成函数对于变换是局部的，尽管变换本身一般不是局部的。因此，这两个局部BRST复形在它们的局部BRST-上同调群可以不同的意义上不是拟同构的。这种差异特别关系到整体守恒量。从非自由规范对称性的BRST复体的观点来看，这些量是BRST精确的，而对于替代复体，这些量是非平凡的余圈。
英文摘要：
The unfree gauge symmetry implies that gauge variation of the action functional vanishes provided for the gauge parameters are restricted by the differential equations. The unfree gauge symmetry is shown to lead to the global conserved quantities whose on shell values are defined by the asymptotics of the fields or data on the lower dimension surface, or even at the point of the space-time, rather than Cauchy hyper-surface. The most known example of such quantity is the cosmological constant of unimodular gravity. More examples are provided in the article for the higher spin gravity analogues of the cosmological constant. Any action enjoying the unfree gauge symmetry is demonstrated to admit the alternative form of gauge symmetry with the higher order derivatives of unrestricted gauge parameters. The higher order gauge symmetry is reducible in general, even if the unfree symmetry is not. The relationship is detailed between these two forms of gauge symmetry in the constrained Hamiltonian formalism. The local map is shown to exist from the unfree gauge algebra to the reducible higher order one, while the inverse map is non-local, in general. The Hamiltonian BFV-BRST formalism is studied for both forms of the gauge symmetry. These two Hamiltonian formalisms are shown connected by canonical transformation involving the ghosts. The generating function is local for the transformation, though the transformation as such is not local, in general. Hence, these two local BRST complexes are not quasi-isomorphic in the sense that their local BRST-cohomology groups can be different. This difference in particular concerns the global conserved quantities. From the standpoint of the BRST complex for unfree gauge symmetry, these quantities are BRST-exact, while for the alternative complex, these quantities are the non-trivial co-cycles.
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