Photon mass in very special relativity

In very special relativity (VSR) a gauge invariant photon mass is allowed. We explore some consequences of keeping this parameter not zero. VSR-Maxwell equations are presented. In addition, we show modifications to the Feynman rules keeping the photon mass and we apply it in the computation of the electron self energy, whose result is free from infrared divergences. A computation of the Coulomb scattering is developed and a small signal of the privileged direction predicted in the theory is present at tree level. Radiative corrections are computed and the photon mass cancels due to soft photon emission as in the standard case.

Figure 1

Examples of vertices in VSR. They come from the perturbative expansion of the nonlocal term $(n·D{)}^{-1}$.

Figure 2

Vertex with $n$ external photonic legs written as the difference between two diagrams with one less leg.

Figure 3

Electron self energy diagrams in VSR.

Figure 4

Loop correction to the vertex.

Figure 5

Ward identity, vertex written as the difference between two propagators with different electron momentum.