Lagrangian cohomological couplings among vector fields and matter fields (Q2784799)

Some new possibilities for analyzing consistent interactions in gauge theories in the framework of the BRST (Becchi-Rouet-Stora extended gauge transformation) cohomology (Batalin, Vilkovisky 1981, 1983, 1985; Henneaux 1990; Henneaux, Teitelboim 1992) are presented. In the paper the consistent Lagrangian couplings between set of vector fields and a system of matter fields are investigated by means of the deformation of the solution of the Batalin-Vilkovisky master equation corresponding to the ``free'' theories (Barnich, Henneaux 1993; Stasheff 1997; Garzia, Knaepen 1998). The former results related to the abelian case (Bizdadea, Cioroianu, Negru, Saliu 2001) are taken into account and extended. As a starting point, a ``free'' action written as the sum of the actions for the vector and matter fields is used. On this basis the corresponding ``free'' Lagrangian BRST differential is constructed, which is found as the sum of the Koshul-Tate differential and the exterior derivative doing the gauge orbits. Then, the first-order as well as the higher-order deformations of the associated solution of the master equation are performed and analyzed in detail. As a result, the consistent couplings between sets of vector and matter fields are obtained. In particular, it is concluded that the interaction terms involving only the vector fields generate the Lagrangian action of Yang-Mills theory, and the first-order couplings between vector \((A^a_\mu)\) and matter \((j^\mu_a)\) fields is of the type \(A^a_\mu j^\mu_a\). The gauge transformation properties of the vector and matter fields are also considered. It is indicated that the overall deformed gauge algebra is a Lie algebra. The developed approach is applied to the two cases of matter fields: real scalar and Dirac fields.