Feynman-Kac-Type Theorems and Gibbs Measures on Path Space

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space
Author: József Lörinczi
Publisher: Walter de Gruyter
Total Pages: 521
Release: 2011-08-29
Genre: Mathematics
ISBN: 3110203731

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.

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space
Author: József Lörinczi
Publisher: Walter de Gruyter
Total Pages: 400
Release: 2016
Genre:
ISBN: 9783110403558

This is the second updated and extended edition of the successful book on Feynman-Kac Theory. It 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. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.

Feynman-Kac-Type Formulae and Gibbs Measures

Feynman-Kac-Type Formulae and Gibbs Measures
Author: József Lörinczi
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 575
Release: 2020-01-20
Genre: Mathematics
ISBN: 3110330393

This is the second updated and extended edition of the successful book on Feynman-Kac theory. It 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. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.

Applications in Rigorous Quantum Field Theory

Applications in Rigorous Quantum Field Theory
Author: Fumio Hiroshima
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 558
Release: 2020-03-09
Genre: Mathematics
ISBN: 3110403544

This is the second updated and extended edition of the successful book on Feynman-Kac theory. It 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. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.

Path Integrals

Path Integrals
Author: Wolfhard Janke
Publisher: World Scientific
Total Pages: 629
Release: 2008
Genre: Science
ISBN: 9812837264

This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.

Gibbs Measures and Phase Transitions

Gibbs Measures and Phase Transitions
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter
Total Pages: 561
Release: 2011
Genre: Measure theory
ISBN: 3110250292

From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou

Stochastic Partial Differential Equations and Related Fields

Stochastic Partial Differential Equations and Related Fields
Author: Andreas Eberle
Publisher: Springer
Total Pages: 565
Release: 2018-07-03
Genre: Mathematics
ISBN: 3319749293

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.