Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles

TL;DR

This paper introduces a nonassociative generalization of principal fiber bundles using smooth loops, enabling the development of gauge theories with higher nonassociative symmetries.

Contribution

It presents a novel framework for principal Q-bundles based on smooth loops, expanding the mathematical foundation of gauge theories.

Findings

Constructed a new class of nonassociative principal bundles.

Demonstrated potential for modeling higher nonassociative symmetries in gauge theories.

Laid groundwork for future nonassociative gauge theory research.

Abstract

A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher ''nonassociative'' symmetries.