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Complete theory of Maxwell and Proca fields

2020; American Physical Society; Volume: 101; Issue: 4 Linguagem: Inglês

10.1103/physrevd.101.045008

2470-0037

Verónica Errasti Díez, Brage Gording, Julio A. Méndez-Zavaleta, Angnis Schmidt-May,

Quantum Electrodynamics and Casimir Effect

We present the most general ghostfree classical Lagrangian containing first-order derivatives and describing interacting real Abelian spin-one fields on Minkowski spacetime. We study both massive Proca and massless Maxwell fields and allow for a nonlinear realization of mass, in the form of derivative self-interactions. Within this context, our construction notoriously extends the existing literature, which is limited to the case of a single Proca field and to multiple interacting Proca fields in the presence of a global rotational symmetry. In the limit of a single Proca field, we reproduce the known healthy interaction terms. We provide the necessary and sufficient conditions to ensure ghost-freedom in any multifield setup. We observe that, in general, the said conditions are not satisfied by the rotationally symmetric multi-Proca interactions suggested so far, which implies that they propagate ghosts. Our theory admits a plethora of applications in a wide range of subjects. For illustrative purposes, we provide concrete proposals in holographic condensed matter and black hole physics.