Modified Euler-Heisenberg effective action and Proper-Time Method in Lorentz-Violating Scalar QED

TL;DR

This paper calculates the one-loop Euler-Heisenberg effective action in Lorentz-violating scalar QED, revealing quantum effects and nonlinear contributions that could influence photon-photon interactions beyond standard QED.

Contribution

It provides the exact all-orders result of the effective action in Lorentz-violating scalar QED, including explicit lower-order evaluations and gauge-invariant Lorentz-violating effects.

Findings

Quantum effects from Lorentz violation are explicitly identified.

Nonlinear Lorentz-violating contributions to photon-photon scattering are evaluated.

Exact all-orders effective action in Lorentz-violating scalar QED is obtained.

Abstract

Quantum photon effects in vacuum provide an interesting setting to test quantum electrodynamics, serving as a source for predictions about physics beyond the Standard Model. In this paper, we investigate these effects by calculating the one-loop Euler-Heisenberg-like effective action within a Lorentz-violating scalar quantum electrodynamics framework. In both CPT-even and CPT-odd scenarios, we obtain the exact result in all orders of the stress tensor $F_{\mu\nu}$ and evaluate explicitly the lower orders of this effective action. We identify the quantum effects coming from Lorentz violation in an explicitly gauge invariant way. Nonlinear Lorentz-violating contributions that may affect photon-photon scattering are explicitly evaluated.