The Geometry of the Master Equation and Topological Quantum Field Theory

  title={The Geometry of the Master Equation and Topological Quantum Field Theory},
  author={M A Alexandrov and Maxim Kontsevich and Albert S. Schwarz and Oleg Zaboronsky},
  journal={International Journal of Modern Physics A},
In Batalin–Vilkovisky 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 QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some construction of QP-manifolds and prove a classification theorem (under certain conditions). We apply these… 

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