TOPOLOGICAL QUANTUM-FIELD THEORIES AND GAUGE-INVARIANCE IN STOCHASTIC QUANTIZATION

The Langevin equations describing the quantization of gauge theories have a geometrical structure. We show that stochastically quantized gauge theories are governed by a single differential operator. The latter combines supersymmetry and ordinary gauge transformations. Quantum field theory can be defined on the basis of a Hamiltonian of the type H = 1/2[Q, QBAR], where Q has has deep relationship with the conserved BRST charge of a topological gauge theory, and QBAR is its adjoint. We display the examples of Yang-Mills theory and of 2D gravity. Interesting applications are for first order actions, in particular for the theories defined by the three dimensional Chern Simons action as well as the "two dimensional" integral-M2 Tr-phi-F.