The Coulomb Gauge in Non-associative Gauge Theory

Authors

Sergey Grigorian, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2024

Abstract

The aim of this paper is to extend existence results for the Coulomb gauge from standard gauge theory to a non-associative setting. Non-associative gauge theory is based on smooth loops, which are the non-associative analogs of Lie groups. The main components of the theory include a finite-dimensional smooth loop L , its tangent algebra l , a finite-dimensional Lie group Ψ , that is the pseudoautomorphism group of L , a smooth manifold M with a principal Ψ -bundle P , and associated bundles Q and A with fibers L and l , respectively. A configuration in this theory is defined as a pair ( s , ω ) , where s is a section of Q and ω is a connection on P . The torsion T ( s , ω ) is the key object in the theory, with a role similar to that of a connection in standard gauge theory. The original motivation for this study comes from G 2 -geometry, and the questions of existence of G 2 -structures with particular torsion types. In particular, given a fixed connection, we prove existence of configurations with divergence-free torsion, given a sufficiently small torsion in a Sobolev norm.

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Recommended Citation

Grigorian, S. The Coulomb Gauge in Non-associative Gauge Theory. J Geom Anal 34, 7 (2024). https://doi.org/10.1007/s12220-023-01445-0

Publication Title

J Geom Anal

DOI

10.1007/s12220-023-01445-0