Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-23
Eur.Phys.J.C70:1153-1164,2010
Physics
High Energy Physics
High Energy Physics - Theory
14 latex pages, no figure, final version for publication in EPJC
Scientific paper
10.1140/epjc/s10052-010-1502-4
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 $\mathbf{E}$ and $\mathbf{B}$ 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 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 .
Ma Bo-Qiang
Shao Lijing
Xiao Zhi
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