Quantization of massive second- and third-rank antisymmetric tensor fields in curved space

We consider massive second- and third-rank antisymmetric tensor fields in arbitrary four-dimensional curved space-time. We perform quantization of these models and evaluation of the effective actions. The massive theories of antisymmetric tensor fields do not possess gauge invariance, which is inherent to massless antisymmetric models. To evaluate the effective actions, we restore gauge invariance in massive theories with the help of the Stückelberg multistep procedure. The result is presented in terms of d’Alembertians acting on a scalar, vector, second- and third-rank antisymmetric tensor fields.