Extravariables in the BRST quantization of second-class constrained systems. Existence theorems

In this paper we show how the BRST quantization can be applied to systems possessing only second-class constraints through their conversion to some first-class ones starting with our method exposed in a previous paper [Nucl. Phys. B 456 (1995) 473]. Thus, it is proved that (i) for a certain class of second-class systems there exists a standard coupling between the variables of the original phase space and some extravariables such that we can transform the original system into a one-parameter family of first-class systems; (ii) the BRST quantization of this family in a standard gauge leads to the same path integral as that of the original system. The analysis is accomplished in both reducible and irreducible cases. At the same time, the Lagrangian action of the first-class family is obtained and its provenance is clarified. In this context, the Wess-Zumino action is also derived. The results from the theoretical part of the paper are exemplified in detail for the massive Yang-Mills theory and for massive abelian three-form gauge fields.