Generation of Carroll-Field-Jackiw term in the Functional Integral approach within Horava-Lifshitz $z=3$ CPT-violating QED

TL;DR

This paper demonstrates how the Carroll-Field-Jackiw term can be generated in a Horava-Lifshitz $z=3$ CPT-violating QED using the functional integral approach, revealing its finiteness and indeterminacy.

Contribution

It introduces a novel application of the functional integral method to induce the CFJ term in a Lorentz and CPT-violating Horava-Lifshitz QED model.

Findings

The CFJ term is finite in this framework.

The CFJ term's coefficient remains undetermined.

Lorentz and CPT breaking are incorporated in the model.

Abstract

In this paper, we apply the functional integral methodology to induce the Carroll-Field-Jackiw (CFJ) term in Horava-Lifshitz $z=3$ CPT-violating QED, where Lorentz and CPT breaking for fermion and photon sectors is introduced, and show that the CFJ term is finite but undetermined.