Starting from a generic Lagrangian, we discuss the number of propagating degrees of freedom in the framework of generalised non-linear electrodynamics when a photon-background split is applied. We start by stating results obtained in a previous paper, before modifying the action to an equivalent form. Within this new formulation, we highlight the presence of an effective mass and consider the mechanical reduction of the model to ensure the positivity of said mass. We then study the constraint algebra of the model and show that we shift from a model with two first-class to two second-class constraints, which implies the propagation of an additional degree of freedom. We also show that the Hamiltonian is bound from below and thus does not suffer from Ostrogradski-type instabilities. We conclude by deriving the propagator for the model, and discussing the potential link between the nature of this additional polarisation and the mechanism behind the effective mass generation in this class of models.

France

Abedennour Dib

Brazil

José Helayël-Neto

Alessandro Spallicci

Generalised non-linear electrodynamics: classical picture and effective mass generation

The total red shift z might be recast as a combination of the expansion red shift and a static shift due to the energy–momentum tensor non-conservation of a photon propagating through Electro-Magnetic (EM) fields. If massive, the photon may be described by the de Broglie–Proca (dBP) theory which satisfies the Lorentz(-Poincaré) Symmetry (LoSy) but not gauge-invariance. The latter is regained in the Standard-Model Extension (SME), associated with LoSy Violation (LSV) that naturally dresses photons of a mass. The non-conservation stems from the vacuum expectation value of the vector and tensor LSV fields. The final colour (red or blue) and size of the static shift depend on the orientations and strength of the LSV and EM multiple fields encountered along the path of the photon. Turning to cosmology, for a zero  $$\Omega _{\Lambda }$$  <math> <msub> <mi>Ω</mi> <mi>Λ</mi> </msub> </math>   energy density, the discrepancy between luminosity and red shift distances of SNeIa disappears thanks to the recasting of z. Massive photons induce an effective dark energy acting ‘optically’ but not dynamically.

Spain

Martín López-Corredoira

Italy

Russia

Salvatore Capozziello

Cosmology and the massive photon frequency shift in the Standard-Model Extension

In the presence of Lorentz Symmetry Violation (LSV) associated with the Standard-Model Extension (SME), we have recently shown the non-conservation of the energy-momentum tensor of a light-wave crossing an Electro-Magnetic (EM) background field even when the latter and the LSV are constant. Incidentally, for a space-time dependent LSV, the presence of an EM field is not necessary. Herein, we infer that in a particle description, the energy non-conservation for a photon implies violation of frequency invariance in vacuo, giving rise to a red or blue shift. We discuss the potential consequences on cosmology.

Frequency variation for in vacuo photon propagation in the Standard-Model Extension

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 ($$V_{\mu }$$ <math><msub><mi>V</mi><mi>μ</mi></msub></math>  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 $$|{\mathbf {V}}|$$ <math><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow></math> . The group velocity exhibits a classic dependency on the inverse of the frequency squared. For the CPT-even classes ($$k_{F}$$ <math><msub><mi>k</mi><mi>F</mi></msub></math>  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 $$k_{F}$$ <math><msub><mi>k</mi><mi>F</mi></msub></math> . 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.

Luca Bonetti

Luís Santos Filho

Photon sector analysis of Super and Lorentz symmetry breaking: effective photon mass, bi-refringence and dissipation