Lorentz Invariance Violation Matrix from a General Principle

TL;DR

This paper derives a Lorentz invariance violation matrix from a principle of physical invariance, leading to modifications in the standard model that suggest extremely small Lorentz violation effects, particularly in proton interactions.

Contribution

It introduces a background matrix derived from a general invariance principle, providing a new way to incorporate Lorentz violation into the standard model.

Findings

Lorentz violation in proton photopion production is about 10^{-23}.

The background matrix induces effective Lorentz-violating terms in the standard model.

The approach offers a theoretical framework for Lorentz invariance violation.

Abstract

We show that a general principle of physical independence or physical invariance of mathematical background manifold leads to a replacement of the common derivative operators by the covariant co-derivative ones. This replacement naturally induces a background matrix, by means of which we obtain an effective Lagrangian for the minimal standard model with supplement terms characterizing Lorentz invariance violation or anisotropy of space-time. We construct a simple model of the background matrix and find that the strength of Lorentz violation of proton in the photopion production is of the order $10^{-23}$.