Stochastic Quantization of Gauge Fields and Constrained Systems
The Parisi-Wu stochastic quantization method is applied to gauge fields and constrained systems. It is first shown, by means of perturbation expansion, that we can quantize non-Abelian Gauge fields without resort to introduction of the conventional gauge fixing term into the Lagrangian, and that the Faddeev-Popov ghost effects can automatically be produced without help of any ghost field. To develop non-perturbative approach to nonlinear fields, we next formulate the general theory of stochastic quantization of a dynamical system with regular Lagrangian under holonomic constraints. Applying it to the nonlinear sigma model, we obtain numerically internal energies and long-range correlation functions using an improved procedure of numerical simulation. Finally we discuss a possible scheme of self-regularized field theory and its renormalization within the framework of the modified stochastic quantization method.
KeywordsLangevin Equation Nonlinear Sigma Model Holonomic Constraint Stochastic Quantization Constraint Surface
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