Overview

Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin turbulent partial differential equations.Errata(s)ErrataForewordForeword (34 KB)Contents: Elementary Aspects of Potential Theory in Mathematical PhysicsScattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: Moller Wave Operators and Asymptotic CompletenessOn the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave PhysicsNonlinear Diffusion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence BehaviorDomains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String TheoryBasic Integral Representations in Mathematical Analysis of Euclidean Functional IntegralsNonlinear Diffusion in RD and Hilbert Spaces: A Path-Integral StudyOn the Ergodic TheoremSome Comments on Sampling of Ergodic Process: An Ergodic Theorem and Turbulent Pressure FluctuationsSome Studies on Functional Integrals Representations for Fluid Motion with Random ConditionsThe Atiyah-Singer Index Theorem: A Heat Kernel (PDE's) ProofReadership: Applied mathematicians, mathematical physicists and theoretical physicists.

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