Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields

TL;DR

This paper explores the connection between Riemann-Finsler geometries and Lorentz-violating scalar field theories, deriving actions and classical particle models, and investigating geometric properties to support conjectures in the field.

Contribution

It establishes a general framework linking Lorentz-violating scalar fields with Riemann-Finsler geometry, including derivation of actions and particle dynamics in arbitrary dimensions.

Findings

Derived the general quadratic action for Lorentz-violating scalar fields.

Constructed classical relativistic point-particle Lagrangians matching quantum dispersion relations.

Investigated properties of Riemann-Finsler spaces related to Lorentz violation.

Abstract

The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results provide support for open conjectures about Riemann-Finsler geometries associated with Lorentz-violating field theories.