Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics (Fundamental Theories of Physics, 13)

over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman­ type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts. Front Matter....Pages i-xviii Front Matter....Pages 1-1 Foundation of the Nonlocal Model of Quantized Fields....Pages 3-45 The Basic Problems of Nonlocal Quantum Field Theory....Pages 46-103 Electromagnetic Interactions in Stochastic Space-Time....Pages 104-133 Four-Fermion Weak Interactions in Stochastic Space-Time....Pages 134-156 Functional Integral Techniques in Quantum Field Theory....Pages 157-209 Front Matter....Pages 211-211 The Basic Concepts of Random Processes and Stochastic Calculus....Pages 213-252 Basic Ideas of Stochastic Quantization....Pages 253-274 Stochastic Mechanics....Pages 275-295 Selected Topics in Stochastic Mechanics....Pages 296-323 Further Developments in Stochastic Quantization....Pages 324-356 Some Physical Consequences of the Hypothesis of Stochastic Space-Time and the Fundamental Length....Pages 357-403 Back Matter....Pages 404-426