On quantum aspects of the higher-derivative Lorentz-breaking extension of QED

TL;DR

This paper investigates the theoretical properties of a higher-derivative Lorentz-breaking extension of QED, analyzing its dynamics, dispersion relations, unitarity, and finite temperature effects to understand its consistency and potential physical implications.

Contribution

It introduces a new scheme for perturbative generation of Lorentz-breaking terms in higher-derivative QED and develops a method to verify unitarity in such theories.

Findings

Unitarity is preserved at one-loop level for specific Lorentz-breaking vectors.

The theory's dispersion relations are explicitly derived.

A finite temperature perturbative scheme is proposed.

Abstract

We consider the higher-derivative Lorentz-breaking extension of QED, where the new terms are the Myers-Pospelov-like ones in gauge and spinor sectors, and the higher--derivative CFJ term. For this theory, we study its tree-level dynamics, discuss the dispersion relation, and present one more scheme for its perturbative generation, including the finite temperature case. Also, we develop a method to study perturbative unitarity based on consistent rotation of the theory to Euclidean space. We use this method to verify explicitly that for special choices of the Lorentz-breaking vector, the unitarity is preserved at the one-loop level, even in the presence of higher time derivatives.