Classical-physics applications for Finsler $b$ space

TL;DR

This paper explores classical physics systems governed by three-dimensional Finsler $b$ space, demonstrating their relevance and potential insights into fermion propagation in Lorentz-violating theories.

Contribution

It identifies classical physics systems governed by 3D Finsler $b$ space and constructs geodesics for non-constant background covectors, showing applications beyond Lorentz violation.

Findings

Classical systems can be governed by 3D Finsler $b$ space.

Existence of geodesics for non-constant covectors.

Potential applications in understanding fermion propagation.

Abstract

The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler $b$ space parametrized by a prescribed background covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler $b$ space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler $b$ spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.