The symplectic quantization of the Cremmer-Scherk-Kalb-Ramond theory

Full text follows: We use the symplectic formalism to quantize the bosonic version of the Cremmer-Scherk-Kalb-Ramond ( CSKR ) supersymmetric theory with a N = 1 in a D = 1+3 space-time. In this theory a scalar, a vector and a tensor field are coupled in a non-trivial way and its quantization appears as a very interesting problem. The Cremmer-Scherk-Kalb-Ramond model has been studied by many theorists. Its quantization has an interesting property: the gauge transformations for the KR fields, characterized by a vector parameter, are not all independent. This is an example of a reducible system and its quantization deserves some care. This reducibility is a providential characteristic of this theory because otherwise it would apparently have zero physical degrees of freedom. In the language of the Dirac constraint formalism, the reducibility is manifested by the fact that not all the first-class constraints are independent. The Dirac method does not present a natural solution for this problem. In a previous work, we have used the Faddeev-Jackiw symplectic formalism (FJ) in the KR gauge theory. We have shown that the elimination of the dependent constraint cannot be applied there, because it would imply a reduction of the number of Lagrange multipliers, which are important in the absorption of superfluous degrees of freedom. The solution we have proposed was the analogue of the BFV and BV methods and introduce a Lagrange multiplier-of-Lagrange multiplier for the reducible relation. The purpose of the present paper is to quantize the CSKR theory, where the tensor, vector and scalar fields are coupled in a non-minimal way. As the KR model, this is also a reducible theory and its quantization is a very non-trivial problem. (author)