QUANTUM-FIELD THEORY WITH FICTITIOUS TIME IN STOCHASTIC QUANTIZATION

A model with spontaneous breakdown of symmetry in quantum field theory is studied in the framework of the Parisi-Wu stochastic quantization (SQ). Looking at the conventional treatment of the model in the canonical and the path-integral quantizations including the problems of many inequivalent Hilbert spaces and measures, we explicitly construct the SQ formulation for the model in the conventional treatment of quantum field theory. The real power of SQ is found in extending quantum field theory beyond the existing frameworks; SQ easily avoids the problems imposed by choices of Hilbert space or measure. We demonstrate it by introducing c-numbers depending on the fictitious time into the starting formal Langevin equations for the model. This new formulation in SQ thus obtained is mathematically well-defined, leading to a definite calculational scheme. The result from this shows that the masses and number of excitation modes change from those in the conventional treatment.