LECTURE NOTES IN APPLIED DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS

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.
Contents: Elementary Aspects of Potential Theory in Mathematical Physics; Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: Möller Wave Operators and Asymptotic Completeness; On the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave Physics; Nonlinear Diffusion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence Behavior; Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String Theory; Basic Integral Representations in Mathematical Analysis of Euclidean Functional Integrals; Nonlinear Diffusion in RD and Hilbert Spaces: A Path-Integral Study; On the Ergodic Theorem; Some Comments on Sampling of Ergodic Process: An Ergodic Theorem and Turbulent Pressure Fluctuations; Some Studies on Functional Integrals Representations for Fluid Motion with Random Conditions; The Atiyah Singer Index Theorem: A Heat Kernel (PDE s) Proof.