Physics – Mathematical Physics
Scientific paper
2012-01-23
Physics
Mathematical Physics
9 pages, no figures; v2: references added
Scientific paper
In this article we investigate parallel transports on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we can construct for every derivation X a module parallel transport along the one-parameter group of algebra automorphisms given by the flow of X. This parallel transport morphism is determined uniquely by a differential equation depending on the covariant derivative along X. Based on this, we define a set of basic gauge invariant observables, i.e. functions from the space of connections to complex numbers. For modules equipped with a hermitian structure, we prove that any hermitian connection can be reconstructed up to gauge equivalence from these observables. This solves the gauge copy problem for gauge theory on hermitian finite projective modules over finite matrix algebras, similar to the Wilson loop observables in gauge theories on commutative smooth manifolds.
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