Metric Gauge Fields in Deformed Special Relativity

TL;DR

This paper explores gauge symmetries in Deformed Special Relativity, revealing metric gauge theories arising from the geometry of energy-dependent deformed Minkowski space, and discusses their geometric properties like curvature and torsion.

Contribution

It introduces the concept of metric gauge theories within DSR, linking gauge symmetries to the geometric structure of deformed Minkowski space and its generalized Lagrange space properties.

Findings

Two types of gauge symmetries identified in DSR.

Internal gauge fields linked to the generalized Lagrange structure.

Curvature and torsion defined in the deformed Minkowski space.

Abstract

We show that, in the framework of Deformed Special Relativity (DSR), namely a (four-dimensional) generalization of the (local) space-time struc- ture based on an energy-dependent "deformation" of the usual Minkowski geometry, two kinds of gauge symmetries arise, whose spaces either coin- cide with the deformed Minkowski space or are just internal spaces to it. This is why we named them "metric gauge theories". In the case of the internal gauge fields, they are a consequence of the deformed Minkowski space (DMS) possessing the structure of a generalized Lagrange space. Such a geometrical structure allows one to define curvature and torsion in the DMS.