Nonrelativistic Quantum Hamiltonian for Lorentz Violation

TL;DR

This paper develops a method to derive the nonrelativistic quantum Hamiltonian for a massive fermion within Lorentz-violating theories, enabling systematic expansion and explicit third-order results.

Contribution

It introduces a systematic approach to obtain the nonrelativistic Hamiltonian from a relativistic Lorentz-violating Lagrangian, including higher-order terms.

Findings

Explicit third-order nonrelativistic Hamiltonian derived.

Method allows extraction of arbitrary order terms in the expansion.

Facilitates analysis of Lorentz violation effects in nonrelativistic quantum systems.

Abstract

A method is presented for deriving the nonrelativistic quantum hamiltonian of a free massive fermion from the relativistic lagrangian of the Lorentz-violating standard-model extension. It permits the extraction of terms at arbitrary order in a Foldy-Wouthuysen expansion in inverse powers of the mass. The quantum particle hamiltonian is obtained and its nonrelativistic limit is given explicitly to third order.