Eur. Phys. J. C 70, 1153-1164 (2010)
https://doi.org/10.1140/epjc/s10052-010-1502-4

Eikonal equation of the Lorentz-violating Maxwell theory

¹ School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, China
² Center for High Energy Physics, Peking University, Beijing, 100871, China

mabq@pku.edu.cn

Received: 9 August 2010
Revised: 1 November 2010
Published online: 20 November 2010

Abstract

We derive the eikonal equation of light wavefront in the presence of Lorentz invariance violation (LIV) from the photon sector of the standard model extension (SME). The results obtained from the equations of the E and B fields, respectively, are the same. This guarantees the self-consistency of our derivation. We adopt a simple case with only one non-zero LIV parameter as an illustration, from which we find two points. One is that, in analogy with the Hamilton–Jacobi equation, from the eikonal equation, we can derive dispersion relations which are compatible with results obtained from other approaches. The other is that the wavefront velocity is the same as the group velocity, as well as the energy flow velocity. If further we define the signal velocity v _s as the front velocity, there always exists a mode with v _s >1; hence causality is violated classically. Thus, our method might be useful in the analysis of Lorentz violation in QED in terms of classical causality.