Heisenberg代数的平坦U（1）丛拓扑类与非纯协变表示
Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra
摘要：
研究了任意流形上海森堡代数的自伴位形空间表示的一般构造。所有这些不等价的表示都用构形空间流形上平坦U（1）丛的拓扑类来参数化。在黎曼流形的情况下，这些表示也是显纯协变的。一般性的讨论，在非相对论性量子力学的一些简单的例子说明，是特别相关的系统，其配置空间参数化的曲线坐标或不是简单的连接，因此包括例如非阿贝尔规范场和重力理论的模空间。
英文摘要：
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.
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