Hamiltonian dynamics of 5D Kalb-Ramond theories with a compact dimension

A detailed Hamiltonian analysis for a five-dimensional Kalb-Ramond, massive Kalb-Ramond and St{\"{u}}eckelberg Kalb-Ramond theories with a compact dimension is performed. We develop a complete constraint program, then we quantize the theory by constructing the Dirac brackets. From the gauge transformations of the theories, we fix a particular gauge and we find pseudo-Goldstone bosons in Kalb-Ramond and St{\"{u}}eckelberg Kalb-Ramond's effective theories. Finally we discuss some remarks and prospects.