Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale

TL;DR

This paper investigates how Lorentz-violation coefficients, specifically $a_nd $b_re affected by spacetime variation in curved backgrounds, deriving a nonrelativistic Hamiltonian and assessing experimental sensitivities.

Contribution

It introduces a framework for analyzing spacetime-dependent Lorentz-violation coefficients in the Standard-Model Extension, focusing on nonrelativistic fermions.

Findings

Derived a nonrelativistic Hamiltonian incorporating coefficient variation.

Identified experimental setups sensitive to spacetime-dependent Lorentz violation.

Provided theoretical tools for testing Lorentz symmetry in curved spacetimes.

Abstract

The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model Extension varying with spacetime position. We focus on two of the coefficients, $a_\mu$ and $b_\mu$, that characterize Lorentz violation in massive fermions, particularly in those fermions that constitute ordinary matter. We calculate the nonrelativistic hamiltonian describing these effects, and use it to extract the sensitivity of several precision experiments to coefficient variation.