Lorentz and CPT violations in Finsler spacetime

TL;DR

This paper develops a model of the Standard Model within Finsler geometry to incorporate Lorentz and CPT violations, explicitly deriving the breaking terms and comparing them with the standard-model extension.

Contribution

It introduces a Finsler geometric framework for Lorentz and CPT violations, explicitly deriving the breaking Lagrangians and relating them to the SME.

Findings

Lorentz violation originates from deviations of the spacetime background from Minkowski.

CPT violation depends on the behavior of the Finsler metric under discrete symmetries.

The Finslerian model aligns with the SME at first order approximation.

Abstract

Standard model with intrinsic Lorentz and CPT violations is proposed in a Finsler geometric framework. We present explicitly Lorentz and CPT--breaking Lagrangians of the matter fields and the gauge fields in locally Minkowski spacetime. The Lorentz invariance violation is found to be originated from the spacetime background deviating from the Minkowski one. Similarly, the CPT violation is determined by the behaviors of the locally Minkowski metric under the parity and time reversal operations. To help understanding phenomenologies, we compare the Finslerian model with the standard--model extension (SME) term by term at a first order approximation.