The Kalb-Ramond field with spontaneous Lorentz symmetry breaking

Abstract

This work provides a study of some aspects of vector and tensor fields as well as their effects in the context of Lorentz spontaneous symmetry breaking. Notably, we have focused on bumblebee models in which there exist a vector field Bμ which acquires a nonzero vacuum expectation value. The study of the antisymmetric tensor, the Kalb-Ramond field, is provided as well showing a similar nonzero vacuum expectation value for the tensor field Bμν. The modified propagator of the Kalb-Ramond field was calculated. To accomplish this, we implemented a closed algebra with six projectors which were the requirement for inverting the wave operator associated with the Lagrangian density of the theory. The massive mode, in agreement with bumblebee models, do not propagate and, therefore, do not contribute to the calculation of the interparticle potential.