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Stochastic theories and deterministic differential equations. (English) Zbl 1201.81084
Summary: We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared.
MSC:
81T08 Constructive quantum field theory
81T10 Model quantum field theories
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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