Hamiltonian analysis of a new massive spin-1 dual model in D-dimensions

Full text: We start from a first-order master action in D-dimensions, recently suggested in the literature, containing one vector field Aμ and one symmetric second-rank tensor ωμν and integrate over ωμν in order to arrive at the Maxwell theory. On the other hand, by integration on the vector field we obtain a constraint equation ∂μωμν = 0 whose general solution when plugged back in the action, gives rise to a higher-rank and higher derivative description of a massless spin-1 particle. This model is dual to the Maxwell theory. We show here that the introduction of a mass term for the vector field (Proca term) in the master action leads on one hand to the Maxwell-Proca theory. On the other hand it gives rise to a massive spin-1 model, second order in derivatives, described by a symmetric second-rank tensor. We analyze the Hamiltonian constraints in this model using the Dirac-Bergmann algorithm and count the degrees of freedom. We compare the physical content of the symmetric tensor model to the Maxwell (massless limit) and Proca theory in the Hamiltonian approach. After it, the last thing we do is to find the local dual map between gauge invariants made out of the fields ωμν and Aμ in the dual models by using the functional generator with external sources. (author)