The complete theory of Maxwell and Proca fields

Understand

We present the most general ghost-free 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 non-linear 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.