Minkowski Stochastic Quantization and Complex Langevin Equation

Abstract

One of the interesting applications of SQM is the quantization of a system with a complex action (Klauder 1983; Parisi 1983). An interest of the complex action exists in two different context: One is connected to a desire to perform the simulation of field theories without doing Wick rotation from Minkowski space to Euclidean space (Hüffel and Rumpf 1984; Gozzi 1985; Nakazato and Yamanaka 1986; Nakazato 1987, for example). On the other hand, even in the Euclidean formulation of field theories, it sometimes happens that the effective action becomes complex. Examples are gauge theory with an external source (Peterson and Sköld 1985; Ambjørn and Yang 1986; Ambjørn, Flensburg and Peterson 1985, 1986), QCD with a chemical potential (Hasenfratz and Karsch 1983), gauge theory with a topological term (Bhanot, Rabinovici, Seiberg and Woit 1984), and so on.