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

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

Arai Asao
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields Book PDF

Author : Arai Asao
Publisher : World Scientific
Page : 892 pages
File Size : 55,6 Mb
Release : 2017-12-20
Category : Science
ISBN : 9789813207134

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Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields by Arai Asao Pdf

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. Contents: Linear Operators on Hilbert SpaceTensor Product of Hilbert SpacesTensor Product of Linear Operators on Hilbert SpacesFull Fock SpaceBoson Fock SpaceFermion Fock SpaceBoson-Fermion Fock SpaceTheory of Infinite-Dimensional Dirac Operators and Abstract Supersymmetric Quantum Fields General Theory of Quantum FieldsQuantum de Broglie FieldQuantum Klein–Gordon FieldQuantum Radiation FieldQuantum Dirac Fieldvan Hove ModelOverview of Interacting Quantum Field Models Readership: Advanced undergraduate and graduate students in mathematics or physics, mathematicians and mathematical physicists. Keywords: Fock Space;Second Quantization;Canonical Commutation Relation;Canonical Anti-Commutation Relation;Quantum Field;Bose Field;Fermi Field;Dirac Operator;Supersymmetry;Supersymmetric Quantum Field; Quantum Electrodynamics;van Hove ModelReview: Key Features: Detailed description of the theory of Fock spaces including full Fock spaces, boson Fock spaces, fermion Fock spaces and boson-fermion Fock spacesNew topics are included, such as the theory of infinite dimensional Dirac operators and an abstract supersymmetric quantum field theory, which have been originally developed by the authorDetailed treatment of mathematical constructions of free quantum field models as well as a simple interacting model

Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields

Asao Arai
Infinite Dimensional Dirac Operators and Supersymmetric Quantum Fields Book PDF

Author : Asao Arai
Publisher : Springer Nature
Page : 123 pages
File Size : 42,9 Mb
Release : 2022-10-18
Category : Science
ISBN : 9789811956782

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Infinite-Dimensional Dirac Operators and Supersymmetric Quantum Fields by Asao Arai Pdf

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.

Infinite-dimensional Dirac Operators and Supersymmetric Quantum Fields

Asao Arai
Infinite dimensional Dirac Operators and Supersymmetric Quantum Fields Book PDF

Author : Asao Arai
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 2022
Category : Quantum field theory
ISBN : 8981195676

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Infinite-dimensional Dirac Operators and Supersymmetric Quantum Fields by Asao Arai Pdf

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 BosonFermion 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 BosonFermion 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.

Mathematical Theory of Quantum Fields

Huzihiro Araki
Mathematical Theory of Quantum Fields Book PDF

Author : Huzihiro Araki
Publisher : OUP Oxford
Page : 254 pages
File Size : 49,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780198517733

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Mathematical Theory of Quantum Fields by Huzihiro Araki Pdf

Quantum field theory is an area of wide and growing interest to students and researchers of both mathematics and physics. This text is an introduction to the subject which uses mathematical theory of operator algebras to present the theory.

Quantum Mechanics and Quantum Field Theory

Jonathan Dimock
Quantum Mechanics and Quantum Field Theory Book PDF

Author : Jonathan Dimock
Publisher : Cambridge University Press
Page : 239 pages
File Size : 54,9 Mb
Release : 2011-02-03
Category : Science
ISBN : 9781139497480

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Quantum Mechanics and Quantum Field Theory by Jonathan Dimock Pdf

Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.

Mathematics of Quantization and Quantum Fields

Jan Dereziński,Christian Gérard
Mathematics of Quantization and Quantum Fields Book PDF

Author : Jan Dereziński,Christian Gérard
Publisher : Cambridge University Press
Page : 687 pages
File Size : 49,7 Mb
Release : 2013-03-07
Category : Science
ISBN : 9781107011113

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Mathematics of Quantization and Quantum Fields by Jan Dereziński,Christian Gérard Pdf

A unique and definitive review of mathematical aspects of quantization and quantum field theory for graduate students and researchers.

Geometric Analysis and Applications to Quantum Field Theory

Peter Bouwknegt,Siye Wu
Geometric Analysis and Applications to Quantum Field Theory Book PDF

Author : Peter Bouwknegt,Siye Wu
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 50,7 Mb
Release : 2002-02-08
Category : Mathematics
ISBN : 0817642870

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Geometric Analysis and Applications to Quantum Field Theory by Peter Bouwknegt,Siye Wu Pdf

In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.

Mathematical Quantum Field Theory and Related Topics

Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada
Mathematical Quantum Field Theory and Related Topics Book PDF

Author : Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 53,7 Mb
Release : 1988
Category : Science
ISBN : 0821860143

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Mathematical Quantum Field Theory and Related Topics by Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada Pdf

Suitable for researchers and advanced graduate students in mathematical physics, this book constitutes the proceedings of a conference on mathematical quantum field theory and related topics. The conference was held at the Centre de Recherches Matheematiques of the Universite de Montreal in September 1987.

Quantum Fields and Processes

John Gough,Joachim Kupsch
Quantum Fields and Processes Book PDF

Author : John Gough,Joachim Kupsch
Publisher : Cambridge University Press
Page : 341 pages
File Size : 49,5 Mb
Release : 2018-04-12
Category : Mathematics
ISBN : 9781108416764

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Quantum Fields and Processes by John Gough,Joachim Kupsch Pdf

Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.

Aspects of Quantum Field Theory in Curved Spacetime

Stephen A. Fulling
Aspects of Quantum Field Theory in Curved Spacetime Book PDF

Author : Stephen A. Fulling
Publisher : Cambridge University Press
Page : 332 pages
File Size : 53,9 Mb
Release : 1989-08-24
Category : Mathematics
ISBN : 0521377684

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Aspects of Quantum Field Theory in Curved Spacetime by Stephen A. Fulling Pdf

The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.

Quantum Field Theory and Gravity

Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler
Quantum Field Theory and Gravity Book PDF

Author : Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 53,7 Mb
Release : 2012-02-08
Category : Mathematics
ISBN : 9783034800433

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Quantum Field Theory and Gravity by Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler Pdf

One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Quantum Field Theory and Topology

Albert S. Schwarz
Quantum Field Theory and Topology Book PDF

Author : Albert S. Schwarz
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 43,8 Mb
Release : 1993-10-21
Category : Mathematics
ISBN : 3540547533

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Quantum Field Theory and Topology by Albert S. Schwarz Pdf

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.

Mathematical Quantum Physics

Gabriele Nunzio Tornetta
Mathematical Quantum Physics Book PDF

Author : Gabriele Nunzio Tornetta
Publisher : Springer Nature
Page : 187 pages
File Size : 50,6 Mb
Release : 2022-10-18
Category : Science
ISBN : 9783031148125

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Mathematical Quantum Physics by Gabriele Nunzio Tornetta Pdf

This book provides the rigorous mathematical foundations of Quantum Physics, from the operational meaning of the measuring process to the most recent theories for the quantum scale of space-time geometry. Topics like relativistic invariance, quantum systems with finite and infinitely many degrees of freedom, second quantisation, scattering theory, are all presented through the formalism of Operator Algebras for a precise mathematical justification. The book is targeted to graduate students and researchers in the area of theoretical/mathematical physics who want to learn about the mathematical foundations of quantum physics, as well as the mathematics students and researchers in the area of operator algebras/functional analysis who want to dive into some of the applications of the theory to physics.

Mathematical Aspects of Quantum Field Theories

Damien Calaque,Thomas Strobl
Mathematical Aspects of Quantum Field Theories Book PDF

Author : Damien Calaque,Thomas Strobl
Publisher : Springer
Page : 572 pages
File Size : 53,5 Mb
Release : 2015-01-06
Category : Science
ISBN : 9783319099491

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Mathematical Aspects of Quantum Field Theories by Damien Calaque,Thomas Strobl Pdf

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Mathematical Theory of Quantum Fields

Huzihiro Araki
Mathematical Theory of Quantum Fields Book PDF

Author : Huzihiro Araki
Publisher : Oxford University Press, USA
Page : 254 pages
File Size : 43,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0198517734

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Mathematical Theory of Quantum Fields by Huzihiro Araki Pdf

Quantum field theory is an area of wide and growing interest to students and researchers of both mathematics and physics. This text is an introduction to the subject which uses mathematical theory of operator algebras to present the theory.