Stochastic Quantization Method in Operator Formalism
Open Access
- 1 June 1983
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 69 (6), 1764-1793
- https://doi.org/10.1143/PTP.69.1764
Abstract
The stochastic quantization method is developed in a possible “Heisenberg” operator theory of stochastic processes so designed as to keep a formal analogy to quantum mechanics. The general theory is first formulated for stochastic processes of the Wiener type and then its application to quantization of boson fields is presented. It seems that the operator formalism is convenient to examine implications of the stochastic quantization method. Within the theoretical framework we develop the “Feynman-Dyson” approach to field propagators in perturbation theory. This approach enables us to simplify and systematize practical calculations in comparison with the Langevin equation method. In the Appendix we formulate the Green function approach to field propagators using the characteristic functional.Keywords
This publication has 4 references indexed in Scilit:
- Stochastic Quantization Method of Fermion FieldsProgress of Theoretical Physics, 1983
- Stochastic Quantization of Non-Abelian Gauge Field: Unitarity Problem and Faddeev-Popov Ghost EffectsProgress of Theoretical Physics, 1983
- On the Quantum Mechanics-like Description of the Theories of the Brownian Motion and Quantum Statistical MechanicsProgress of Theoretical Physics, 1956
- On the Green’s functions of quantized fields. IProceedings of the National Academy of Sciences, 1951