TOPOLOGICAL YANG-MILLS THEORY WITH VECTOR AND ANTISYMMETRIC TENSOR-FIELDS

We study a system composed of vector and second rank antisymmetric tenser gauge fields in the superconnection framework. We incorporate the matrix derivative of non-commutative geometry in order to induce the topological Yang-Mills theory. In this structure we get the BRST and anti-BRST transformation rules from one horizontality condition, and obtain the topological classical action naturally from the extended field strength. We obtain its quantum action through the BRST formalism.