Physicality of the effective mass after quantization

Determine whether the effective photon mass generated by the Generalised Non-Linear Electrodynamics model remains physical after quantization, including whether coupling the theory to fermions and constructing the corresponding Feynman rules establishes a genuine mass rather than a classical effective artifact.

Background

The paper establishes, at the classical level, that the Generalised Non-Linear Electrodynamics model can exhibit a massive pole and a mass gap while preserving gauge invariance, maintaining two physical degrees of freedom, and possessing a positive-definite Hamiltonian for purely space-like background vectors. The authors nevertheless leave unresolved whether this mass survives quantization. They specifically identify possible quantum anomalies and the need to couple fermions consistently, since the non-dynamical background that modifies photon propagation should also affect fermionic dynamics. Constructing a fermionic representation and deriving the appropriate Feynman rules are presented as necessary steps toward deciding whether the mass is physically realized or only an artifact of the classical description.

References

The unanswered question here is considering the physicality of the mass. Indeed, we showed that classically, the theory is well behaved (from the dispersion relations, poles, and Hamiltonian in pure space-like case), but quantisation can introduce anomalies and might cast shadow on the massiveness of the model. The next step is to couple fermions to the theory, which might not be as trivial as it seems. Indeed, finding a fermionic representation might appear simple, but we have to keep in mind that if the effects of the background on photons are not trivial, they should also be non trivial on fermions. Once fully quantised, and with the proper Feynman rules in hand, we could finally state if our mass is physical, or simply an effective artifact that only holds at the classical level.

— Dispersion relation, propagation features and canonical gauge structure of GNLED  (2609.39470 - Dib et al., 30 Sep 2026) in Section Discussion