Gauge Theories with Cayley-Klein $SO(2;j)$ and $SO(3;j)$ Gauge Groups

TL;DR

This paper explores gauge theories based on Cayley-Klein groups $SO(2;j)$ and $SO(3;j)$, showing that contracted non-semisimple groups yield simpler interactions while maintaining the same particle spectrum as the original theories.

Contribution

It demonstrates that gauge theories with contracted Cayley-Klein groups can be simplified without altering the particle content, extending the understanding of non-semisimple gauge symmetries.

Findings

Contracted gauge theories describe the same particle spectrum as original theories.

Non-semisimple groups lead to simpler field interactions.

Matter spaces become fiber spaces with degenerate metrics.

Abstract

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.