Abstract
Within the standard model extension (SME), we expand our previous findings on four classes of violations of Super-Symmetry (SuSy) and Lorentz Symmetry (LoSy), differing in the handedness of the Charge conjugation-Parity-Time reversal (CPT) symmetry and in whether considering the impact of photinos on photon propagation. The violations, occurring at the early universe high energies, show visible traces at present in the Dispersion Relations (DRs). For the CPT-odd classes (V_{mu } breaking vector) associated with the Carroll–Field–Jackiw (CFJ) model, the DRs and the Lagrangian show for the photon an effective mass, gauge invariant, proportional to |{mathbf {V}}|. The group velocity exhibits a classic dependency on the inverse of the frequency squared. For the CPT-even classes (k_{F} breaking tensor), when the photino is considered, the DRs display also a massive behaviour inversely proportional to a coefficient in the Lagrangian and to a term linearly dependent on k_{F}. All DRs display an angular dependence and lack LoSy invariance. In describing our results, we also point out the following properties: (i) the appearance of complex or simply imaginary frequencies and super-luminal speeds and (ii) the emergence of bi-refringence. Finally, we point out the circumstances for which SuSy and LoSy breakings, possibly in presence of an external field, lead to the non-conservation of the photon energy-momentum tensor. We do so for both CPT sectors.
Highlights
For the most part, we base our understanding of particle physics on the standard model (SM)
We notice that the photon is the only massless nonconfined Boson; the reason for this must at least be questioned by fundamental physics
Between the GeV scale of the electroweak interactions and the Grand Unification Theory (GUT) scale (1016 GeV), it is widely believed that new physics should appear at the TeV scale, which is the experimental limit up to which the SM was tested [7]
Summary
We shall encounter real frequencies sub- and luminal velocities and imaginary and complex frequencies, and superluminal velocities.. The photon is dressed of an effective mass, that we shall see, depends on the perturbation vector or ten-. Letting rest mass and rest frequency real, mass and energy become imaginary. More recent literature adopts kμAF and kμFνρσ for LSV vector and tensor, respectively, we drop the former in favour of V μ for simplicity of notation especially when addressing time or space components and normalised units. 1.2 Upper limits on Vμ vector and photon mass mγ Ground based experiments indicate that |V|, the space components, must be smaller than 10−10 eV = 1.6 × 10−29 J from the bounds given by the energy shifts in the spectrum of the hydrogen atom [67]; else smaller than 8 × 10−14 eV = 1, 3 × 10−32 J from measurements of the rotation in the polarisation of light in resonant cavities [67]. The actual Particle Data Group (PDG) limit on photon mass [68] refers to values obtained in [69,70] of 10−54 kg or 5.6 × 10−19 eV/c2, to be taken with some care, as motivated in [71,72,73]
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