Basic Ideas of Stochastic Quantization
In recent years interest has significantly increased in the investigation of stochastic processes and fields. This is due in the first place to the fact that it has been possible to establish an intimate connection between the theory of stochastic processes, quantum mechanics (Fényes, 1952; Kershaw, 1964; Nelson, 1966, 1967; de la Peña-Auerbach, 1969; de la Peña-Auerbach and Cetto, 1974, 1975, 1982; Davidson, 1979; Moore, 1979; Yasue, 1979; Lee, 1980; Santamato and Lavenda, 1981; Claverie and Diner, 1973, 1975, and others), and Euclidean quantum field theory (Nelson, 1973; Dohrn and Guerra, 1978; Guerra and Ruggiero, 1973), known under the general name of the stochastic quantization of systems (stochastic mechanics) stochastic quantum mechanics. Studies have been made on the generalization of the ideas of the stochastic quantization of Nelson and Fényes for continuous systems and fields (i.e., for systems with an infinite number of degrees of freedom) (Guerra and Ruggiero, 1973; Dohrn and Guerra, 1978; Dankel, 1970, 1977; Moore, 1980 and Davidson, 1980–82), and also for particles with spin (Dankel, 1970, 1977; de la Peña-Auerbach, 1971) and relativistic mechanics (Caubet, 1976; Aron, 1966; Lehr and Park, 1977; Guerra and Ruggiero, 1978; Vigier, 1979 and Namsrai, 1980a).
KeywordsStochastic Mechanic Stochastic Quantization Wightman Function Stochastic Electrodynamic Stochastic Space
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