B-V QUANTIZATION AND FIELD-ANTI-FIELD DUALITY FOR P-FORM GAUGE-FIELDS, TOPOLOGICAL FIELD-THEORIES AND 2D GRAVITY

We construct a framework which unifies in pairs the fields and anti-fi elds of the Batalin and Vilkovisky quantization method. We consider ga uge theories of p-forms coupled to Yang-Mills fields. Our algorithm ge nerates many topological models of the Chem-Simons type or of the Dona ldson-Witten type, Some of these models can undergo a partial breaking of their topological symmetries. We investigate the properties of 2D gravity in the Batalin and Vilkovisky quantization scheme. We find a s tructure which satisfies the holomorphic factorization and also proper ties analogous to those existing in the topological theories of forms. New conformal fields are introduced with their invariant action.