Lörinczi / Hiroshima / Betz Feynman-Kac-Type Theorems and Gibbs Measures on Path Space

With Applications to Rigorous Quantum Field Theory
1. Auflage 2011
ISBN: 978-3-11-020373-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 34, 516 Seiten, Gewicht: 10 g

Reihe: De Gruyter Studies in Mathematics

This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. These ideas are then applied principally to a rigorous treatment of some fundamental models of quantum field theory.

In this self-contained presentation of the material both beginners and experts are addressed, while putting emphasis on the interdisciplinary character of the subject.

Zielgruppe

Graduate Students, Lecturers, and Researchers in Mathematics; Aca

Autoren/Hrsg.

Lörinczi, József

Hiroshima, Fumio

Betz, Volker

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Frontmatter
Preface
Contents
Part I Feynman–Kac-type theorems and Gibbs measures
Chapter 1 Heuristics and history
Chapter 2 Probabilistic preliminaries
Chapter 3 Feynman–Kac formulae
Chapter 4 Gibbs measures associated with Feynman–Kac semigroups
Part II Rigorous quantum field theory
Chapter 5 Free Euclidean quantum field and Ornstein–Uhlenbeck processes
Chapter 6 The Nelson model by path measures
Chapter 7 The Pauli–Fierz model by path measures
Chapter 8 Notes and References
Bibliography
Index

Über Autor(innen)

József Lorinczi, Loughborough University, UK; Fumio Hiroshima, University of Kyushu, Fukuoka, Japan; Volker Betz, University of Warwick, Coventry, UK.