Mathematical Theory of Feynman Path Integrals An Introduction /

• Κύριοι συγγραφείς: Albeverio, Sergio A. (Συγγραφέας), Høegh-Krohn, Raphael J. (Συγγραφέας), Mazzucchi, Sonia (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Σειρά: Lecture Notes in Mathematics, 523
• Θέματα: Mathematics.; Functional analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Integral equations.; Measure theory.; Operator theory.; Probabilities.; Integral Equations.; Measure and Integration.; Functional Analysis.; Operator Theory.; Probability Theory and Stochastic Processes.; Global Analysis and Analysis on Manifolds.

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an...

Πίνακας περιεχομένων:

• Preface to the second edition
• Preface to the first edition
• 1.Introduction
• 2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa
• 3.The Feynman Path Integral in Potential Scattering
• 4.The Fresnel Integral Relative to a Non-singular Quadratic Form
• 5.Feynman Path Integrals for the Anharmonic Oscillator
• 6.Expectations with Respect to the Ground State of the Harmonic Oscillator
• 7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator
• 8.The Invariant Quasi-free States
• 9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field
• 10.Some Recent Developments
• 10.1.The infinite dimensional oscillatory integral
• 10.2.Feynman path integrals for polynomially growing potentials
• 10.3.The semiclassical expansio
• 10.4.Alternative approaches to Feynman path integrals
• 10.4.1.Analytic continuation
• 10.4.2.White noise calculus
• 10.5.Recent applications
• 10.5.1.The Schroedinger equation with magnetic fields
• 10.5.2.The Schroedinger equation with time dependent potentials
• 10.5.3 .hase space Feynman path integrals
• 10.5.4.The stochastic Schroedinger equation
• 10.5.5.The Chern-Simons functional integral
• References of the first edition
• References of the second edition
• Analytic index
• List of Notations.