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Worldline Approach of Topological BF Theory

Ichiro Oda·Mario Tonin
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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 antifields and ghosts as geometrical and elementary objects.

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Ichiro Oda, Mario Tonin. 2005-06-14. Worldline Approach of Topological BF Theory. https://doi.org/10.1016/j.physletb.2005.07.037

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