Module parallel transports in fuzzy gauge theory

Schenkel, Alexander

Abstract

In this paper, 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. © World Scientific Publishing Company.

Citation

Schenkel, A. (2014). Module parallel transports in fuzzy gauge theory. International Journal of Geometric Methods in Modern Physics, 11(03), Article 1450021. https://doi.org/10.1142/S0219887814500212

• Journal Article Type: Article
• Acceptance Date: Sep 19, 2013
• Online Publication Date: Oct 28, 2013
• Publication Date: 2014-03
• Deposit Date: Aug 22, 2019
• Journal: International Journal of Geometric Methods in Modern Physics
• Print ISSN: 0219-8878
• Electronic ISSN: 1793-6977
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 11
• Issue: 03
• Article Number: 1450021
• DOI: https://doi.org/10.1142/S0219887814500212
• Keywords: Mathematical Physics; High Energy Physics - Theory
• Public URL: https://nottingham-repository.worktribe.com/output/2460559
• Publisher URL: https://www.worldscientific.com/doi/abs/10.1142/S0219887814500212