Lorentz symmetry violating low energy dispersion relations from a dimension-five photon scalar mixing operator

TL;DR

This paper investigates how dimension-five photon-scalar interactions can lead to Lorentz symmetry violations in low-energy dispersion relations, revealing superluminal propagation and instabilities, with potential astrophysical consequences.

Contribution

It identifies energy intervals where causality and stability are preserved in photon-scalar mixing, using optical and gravitational techniques to analyze dispersion relations.

Findings

Superluminal phase velocities occur outside certain energy ranges.

Stability is restored within specific energy intervals.

Potential astrophysical implications of Lorentz violation are discussed.

Abstract

Dimension-five photon $(\gamma )$ scalar $(\phi)$ interaction terms usually appear in the bosonic sector of unified theories of electromagnetism and gravity. In these theories the three propagation eigenstates are different from the three field eigenstates. The dispersion relation in an external magnetic field shows that, for a non- zero energy $(\omega)$, out of the three propagating eigenstates one has superluminal phase velocity $v_p$. During propagation, another eigenstate undergoes amplification or attenuation, showing signs of an unstable system. The remaining one maintains causality. In this paper, using techniques from optics as well as gravity, we identify the energy $(\omega)$ interval outside which $v_p \le c$ for the field eigenstates $|\gamma_{\parallel} > $ and $ |\phi > $, and stability of the system is restored. The behavior of group velocity $v_g$ is also explored in the same context. We conclude by pointing out its possible astrophysical implications.