Stochastic quantization method and field theory

Stochastic quantization of field theory is discussed from both perturbative and non-perturbative view points. In the perturbative approach, we investigate in detail characteristic features of the stochastic quantization method applied to the scalar field, the Abelian and the non-Abelian gauge fields and the gravitational field. This leads us to an important result: that the method enables us to quantize the gauge theory without gauge fixing and ghost field. For the non-perturbative approach, we reformulate the theoretical framework of the stochastic quantization to be applicable to numerical simulations. Through practical application of the formalism to nonlinear σ-model, it is pointed out that the Langevin equation in the stochastic quantization gives us a new powerful method of numerical simulation. (author)