Extended form method of antifield-BRST formalism for topological quantum field theories

Abstract

We present a concise method to construct a BRST invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution for the master equation is directly obtained by means of the extended forms that involve all the required ghosts and antifields. The BV actions for the non-abelian $BF$ theories (in 4 and higher dimensions) and the Chern-Simons theory are constructed by means of the extended form method. An extension of the $BF$ theory in 4-dimensions to include a ``cosmological term'' is also examined and the close connection with the topological Yang-Mills theory is indicated.