Threshold analyses and Lorentz violation

TL;DR

This paper examines the theoretical foundations of Lorentz violation, focusing on threshold analyses, coordinate invariance, and causality, to refine the search for observable Lorentz-breaking effects.

Contribution

It introduces a framework that excludes many previously considered Lorentz-breaking parameters and advances the methodology for dispersion-relation investigations.

Findings

Excludes several Lorentz-breaking parameters based on fundamental principles

Highlights the importance of coordinate invariance and causality in Lorentz violation studies

Proposes a viable approach for dispersion-relation investigations

Abstract

In the context of threshold investigations of Lorentz violation, we discuss the fundamental principle of coordinate invariance, the role of an effective dynamical framework, and the conditions of positivity and causality. Our analysis excludes a variety of previously considered Lorentz-breaking parameters and opens an avenue for viable dispersion-relation investigations of Lorentz violation.