Abstract
We present a worldline description of topological non-Abelian BF theory in arbitrary space–time dimensions. It is shown that starting with a trivial classical action defined on the worldline, the BRST cohomology has a natural representation as the sum of the de Rham cohomology. Based on this observation, we construct a second-quantized action of the BF theory. Interestingly enough, this theory naturally gives us a minimal solution to the Batalin–Vilkovisky master equation of the BF theory. Our formalism sheds some light not only on an interplay between the Witten-type and the Schwarz-type topological quantum field theories but also on the role of the Batalin–Vilkovisky anti-fields and ghosts as geometrical and elementary objects.
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