Stochastic quantization of field theory

A new quantization procedure based on the analogy between quantum theory and nonequilibrium statistical mechanics is described. Stochastic quantization is particularly useful for gauge theories, including lattice theories. Both the theoretical basis of the method and its computer implementation are discussed. A detailed discussion is given of applications to reduced Eguchi–Kawai models, which correspond to lattice quantum chromodynamics in the limit of an infinite number of colors. The complex stochastic equation corresponding to quantum theory in the ordinary Minkowski space is also examined. The equations are discussed in curved field space, as are the difference equations that replace the stochastic equation with a high degree of precision.