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

Published: 2011-08-29

Total Pages: 521

ISBN-13: 3110203731

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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

Published: 2016

Total Pages: 400

ISBN-13: 9783110403558

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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

Published: 2020-01-20

Total Pages: 575

ISBN-13: 3110330393

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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

Published: 2020-03-09

Total Pages: 558

ISBN-13: 3110403544

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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

Published: 2008

Total Pages: 629

ISBN-13: 9812837264

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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

Published: 2011

Total Pages: 561

ISBN-13: 3110250292

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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

Published: 2018-07-03

Total Pages: 565

ISBN-13: 3319749293

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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.

Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields
Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields

Author: Asao Arai

Publisher: Springer Nature

Published: 2022-10-18

Total Pages: 123

ISBN-13: 9811956782

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This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract Boson–Fermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous analysis of them. The importance and the relevance of the subject are that in physics literature, supersymmetric quantum field models are only formally (heuristically) considered and hence may be ill-defined mathematically. From a mathematical point of view, however, they suggest new aspects related to infinite-dimensional geometry and analysis. Therefore, it is important to show the mathematical existence of such models first and then study them in detail. The book shows that the theory of the abstract Boson–Fermion Fock space serves this purpose. The analysis developed in the book also provides a good example of infinite-dimensional analysis from the functional analysis point of view, including a theory of infinite-dimensional Dirac operators and Laplacians.