The Geometry of the Master Equation and Topological Quantum Field Theory
Abstract
In BatalinVilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QPmanifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Qinvariant odd symplectic structure. We study geometry of QPmanifolds. In particular, we describe some construction of QPmanifolds and prove a classification theorem (under certain conditions).
We apply these geometric constructions to obtain in a natural way the action functionals of twodimensional topological sigmamodels and to show that the ChernSimons theory in BVformalism arises as a sigmamodel with target space Π { G}. (Here G stands for a Lie algebra and Π denotes parity inversion.)
 Publication:

International Journal of Modern Physics A
 Pub Date:
 1997
 DOI:
 10.1142/S0217751X97001031
 arXiv:
 arXiv:hepth/9502010
 Bibcode:
 1997IJMPA..12.1405A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 29 pages, Plain TeX, minor modifications in English are made by Jim Stasheff, some misprints are corrected, acknowledgements and references added