Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields (Second Edition)

Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields (Second Edition)

Author: Asao Arai

Publisher: World Scientific

Published: 2024-09-03

Total Pages: 1115

ISBN-13: 9811288453

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This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.


Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields

Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields

Author: Asao Arai

Publisher: World Scientific

Published: 2017-12-20

Total Pages: 893

ISBN-13: 9813207132

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This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.


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.


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.


Mathematical Theory of Feynman Path Integrals

Mathematical Theory of Feynman Path Integrals

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

Published: 2008-05-30

Total Pages: 184

ISBN-13: 3540769544

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The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.


Quantum Field Theory for Economics and Finance

Quantum Field Theory for Economics and Finance

Author: B. E. Baaquie

Publisher: Cambridge University Press

Published: 2018-08-23

Total Pages: 717

ISBN-13: 1108423159

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This book provides an introduction to how the mathematical tools from quantum field theory can be applied to economics and finance. Providing a range of quantum mathematical techniques for designing financial instruments, it demonstrates how a range of topics have quantum mechanical formulations, from asset pricing to interest rates.


Festschrift Masatoshi Fukushima: In Honor Of Masatoshi Fukushima's Sanju

Festschrift Masatoshi Fukushima: In Honor Of Masatoshi Fukushima's Sanju

Author: Zhen-qing Chen

Publisher: World Scientific

Published: 2014-11-27

Total Pages: 618

ISBN-13: 981459654X

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This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.


Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory

Author: Philippe Andre Martin

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 442

ISBN-13: 3662084902

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Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a substantially new treatment of nucleon pairing.


Progress in Physics, vol. 3/2015

Progress in Physics, vol. 3/2015

Author: Dmitri Rabounski

Publisher: Infinite Study

Published:

Total Pages: 96

ISBN-13:

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The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics