Hamiltonian dynamics for Proca's theories in five dimensions with a compact dimension

Abstract

The canonical analysis of Proca's theory in five dimensions with a compact dimension is performed. From the Proca five dimensional action, we perform the compactification process on a $S^1/\mathbf{Z_2}$ orbifold, then, we analyze the four dimensional effective action that emerges from the compactification process. We report the extended action, the extended Hamiltonian and we carry out the counting of physical degrees of freedom of the theory. We show that the theory with the compact dimension continues laking of first class constraints. In fact, the final theory is not a gauge theory and describes the propagation of a massive vector field plus a tower of massive $KK$-excitations and one massive scalar field. Finally, we develop the analysis of a 5D $BF$-like theory with a Proca mass term, we perform the compactification process on a $S^1/\mathbf{Z_2}$ orbifold and we find all the constraints of the effective theory, we also carry out the counting of physical degrees of freedom; with these results, we show that the theory is not topological but reducible in the first class constraints.