1201.4785 (Alexander Schenkel)

Parallel transport observables for connections on finite projective
modules over matrix algebras    [PDF]

Alexander Schenkel

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.

View original: http://arxiv.org/abs/1201.4785