Mathematical Aspects Of Quantum Field Theory
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Aspects Of Quantum Field Theory In Curved Spacetime
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Author : Stephen A. Fulling
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-24
Aspects Of Quantum Field Theory In Curved Spacetime written by Stephen A. Fulling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-24 with Mathematics categories.
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 For Mathematicians
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Author : Robin Ticciati
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-13
Quantum Field Theory For Mathematicians written by Robin Ticciati and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-13 with Mathematics categories.
This should be a useful reference for anybody with an interest in quantum theory.
Mathematical Aspects Of Quantum Field Theory
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Author : Edson de Faria
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Mathematical Aspects Of Quantum Field Theory written by Edson de Faria and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Science categories.
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Non Perturbative Quantum Field Theory
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Author : Jürg Fröhlich
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1992
Non Perturbative Quantum Field Theory written by Jürg Fröhlich and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes
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Author : Gerhard Grensing
language : en
Publisher: World Scientific
Release Date : 2021-07-15
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes written by Gerhard Grensing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Science categories.
The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields Second Edition
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Author : Asao Arai
language : en
Publisher: World Scientific
Release Date : 2024-09-03
Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields An Introduction To Mathematical Analysis Of Quantum Fields Second Edition written by Asao Arai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-03 with Mathematics categories.
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.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
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.
Analytic Aspects Of Quantum Fields
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Author : Andrei A Bytsenko
language : en
Publisher: World Scientific
Release Date : 2003-10-14
Analytic Aspects Of Quantum Fields written by Andrei A Bytsenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-14 with Science categories.
One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.
Quantum Field Theory
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Author : G. B. Folland
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-08-26
Quantum Field Theory written by G. B. Folland and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-26 with Mathematics categories.
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.
Ontological Aspects Of Quantum Field Theory
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Author : Meinard Kuhlmann
language : en
Publisher: World Scientific
Release Date : 2002-11-26
Ontological Aspects Of Quantum Field Theory written by Meinard Kuhlmann and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-26 with Science categories.
Quantum field theory (QFT) provides the framework for many fundamental theories in modern physics, and over the last few years there has been growing interest in its historical and philosophical foundations. This anthology on the foundations of QFT brings together 15 essays by well-known researchers in physics, the philosophy of physics, and analytic philosophy.Many of these essays were first presented as papers at the conference “Ontological Aspects of Quantum Field Theory”, held at the Zentrum für interdisziplinäre Forschung (ZiF), Bielefeld, Germany. The essays contain cutting-edge work on ontological aspects of QFT, including: the role of measurement and experimental evidence, corpuscular versus field-theoretic interpretations of QFT, the interpretation of gauge symmetry, and localization.This book is ideally suited to anyone with an interest in the foundations of quantum physics, including physicists, philosophers and historians of physics, as well as general readers interested in philosophy or science.