Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics

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Fundamental Theories of Physics 13

ISBN:	9027720010
ISBN 13:	9789027720016
Autor:	Namsrai, K H
Verlag:	Springer Verlag GmbH
Umfang:	xviii, 426 S.
Erscheinungsdatum:	31.12.1985
Produktform:	Gebunden/Hardback
Einband:	Gebunden

InhaltsangabeI: Nonlocal Quantum Field Theory.- I/Foundation of the Nonlocal Model of Quantized Fields.- 1.1. Introduction.- 1.2. Stochastic Space-Time.- 1.3. The Method of Averaging in Stochastic Space-Time and Nonlocality.- 1.4. The Class of Test Functions and Generalized Functions.- 1.4.1. Introduction.- 1.4.2. Space of Test Functions.- 1.4.3. Linear Functional and Generalized Functions.- 1.4.3a. General Definition.- 1.4.3b. Transformation of the Arguments and Differentiation of the Generalized Functions.- 1.4.3c. The Fourier Transform of Generalized Functions.- 1.4.3d. Multiplication of the Generalized Functions by a Smooth Function and Their Convolution.- 1.4.4. Generalized Functions of Quantum Field Theory.- 1.4.5.The Class of Test Functions in the Nonlocal Case.- 1.4.6. The Class of Generalized Functions in the Nonlocal Case.- 2/The Basic Problems of Nonlocal Quantum Field Theory.- 2.1. Nonlocality and the Interaction Lagrangian.- 2.2. Quantization of Nonlocal Field Theory.- 2.2.1. Formulation of the Quantization Problem.- 2.2.2. Regularization Procedure.- 2.2.3. Quantization of the Regularized Equation.- 2.2.4. Green Functions of the Field ??(x).- 2.2.5. The Interacting System Before Removal of the Regularization.- 2.2.6. The Green Functions in the Limit ??0.- 2.3. The Physical Meaning of the Form Factors.- 2.4.The Causality Condition and Unitarity of the S-Matrix in Nonlocal Quantum Field Theory.- 2.4.1. Introduction.- 2.4.2. The Causality Condition.- 2.4.3. The Scheme of Proof of Unitarity of the S-Matrix in Perturbation Theory.- 2.4.4. An Intermediate Regularization Scheme.- 2.4.5. Proof of the Unitarity of the S-Matrix in a Functional Form.- 2.5. The Schrödinger Equation in Quantum Field Theory with Nonlocal Interactions.- 2.5.1. Introduction.- 2.5.2. The Field Operator at Imaginary Time.- 2.5.3. The State Space at Imaginary Time.- 2.5.4. The Interaction Hamiltonian and the Evolution Equation.- 2.5.5. Appendix A.- 3/Electromagnetic Interactions in Stochastic Space-Time.- 3.1. Introduction.- 3.2. Gauge Invariance of the Theory and Generalization of Kroll’s Procedure.- 3.3. The Interaction Lagrangian and the Construction of the S-Matrix.- 3.4. Construction of a Perturbation Series for the S-Matrix in Quantum Electrodynamics.- 3.4.1. The Diagrams of Vacuum Polarization.- 3.4.2. The Diagram of Self-Energy.- 3.4.3. The Vertex Diagram and the Corrections to the Anomalous Magnetic Moment (AMM) of Leptons and to the Lamb Shift.- 3.5 The Electrodynamics of Particles with Spins 0 and 1.- 3.5.1. Introduction.- 3.5.2. The Diagrams of the Vacuum Polarization of Boson Fields.- 3.5.3. The Self-Energy of Bosons.- 4/Four-Fermion Weak Interactions in Stochastic Space-Time.- 4.1. Introduction.- 4.2. Gauge Invariance for the S-Matrix in Stochastic-Nonlocal Theory of Weak Interactions.- 4.3. Calculation of the ‚Weak‘ Corrections to the Anomalous Magnetic Moment (AMM) of Leptons.- 4.4. Some Consequences of Neutrino Oscillations in Stochastic- Nonlocal Theory.- 4.4.1. Introduction.- 4.4.2. The $\mu\rightarrow 3e$ Decay.- 4.4.3. The $K_{L}^{0}\rightarrow\mu e$ Decay.- 4.5. Neutrino Electromagnetic Properties in the Stochastic-Nonlocal Theory of Weak Interactions.- 4.6. Studies of the Decay $K_{L}^{0}\rightarrow\mu^{+}\mu^{-}$ and $K_{L}^{0}$- and $K_{S}^{0}$-Meson Mass Difference.- 4.6.1. Introduction.- 4.6.2. The $K_{L}^{0}\rightarrow\mu^{+}\mu^{-}$ Decay.- 4.6.3. The Mass Difference of $K_{L}^{0}$- and $K_{S}^{0}$-Mesons.- 4.7. Appendix B. Calculation of the Contour Integral.- 5/Functional Integral Techniques in Quantum Field Theory.- 5.1. Mathematical Preliminaries.- 5.2. Historical Background of Path Integrals.- 5.3. Analysis on a Finite-Dimensional Grassmann Algebra.- 5.3.1. Definition.- 5.3.2. Derivatives.- 5.3.3. Integration over a Grassmann Algebra (Finite-Dimensional Case).- 5.4. Grassmann Algebra with an Infinite Number of Generators.- 5.4.1. Definition.- 5.4.2. Grassmann Algebra with Involution.- 5.4.3. Functional (or Variational) Derivativ

Artikelnummer: 1587289 Kategorie: Theoretische Physik

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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.