模糊规范理论中的模并行输运
Module parallel transports in fuzzy gauge theory
摘要：
本文定义并研究了有限矩阵代数上有限投射模的平行迁移概念。给定代数上的一个基于导子的微分和模上的一个联络，我们对每个导子X构造一个模并行迁移，它是X生成的单参数代数自同构群的模的提升.这种平行输运态射由依赖于沿X的协变导数的常微分方程唯一地确定。基于这些平行输运态射，我们定义了一组基本的规范不变观测量，即从连接空间到复数的函数。对于配备了厄米结构的模块，我们证明了这组可观的空间上的厄米连接的规范等价类是分离的。这解决了模糊规范理论的规范复制问题。
英文摘要：
In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every derivation X a module parallel transport, which is a lift to the module of the one-parameter group of algebra automorphisms generated by X. This parallel transport morphism is determined uniquely by an ordinary differential equation depending on the covariant derivative along X. Based on these parallel transport morphisms, we define a basic set of gauge invariant observables, i.e. functions from the space of connections to the complex numbers. For modules equipped with a hermitian structure, we prove that this set of observables is separating on the space of gauge equivalence classes of hermitian connections. This solves the gauge copy problem for fuzzy gauge theories.
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