Towards The Mathematics Of Quantum Field Theory

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Towards the Mathematics of Quantum Field Theory

Frédéric Paugam
Towards the Mathematics of Quantum Field Theory Book PDF

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 52,7 Mb
Release : 2014-02-20
Category : Science
ISBN : 9783319045641

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Towards the Mathematics of Quantum Field Theory by Frédéric Paugam Pdf

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Quantum Field Theory: A Tourist Guide for Mathematicians

Gerald B. Folland
Quantum Field Theory A Tourist Guide for Mathematicians Book PDF

Author : Gerald B. Folland
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 50,5 Mb
Release : 2021-02-03
Category : Education
ISBN : 9781470464837

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Quantum Field Theory: A Tourist Guide for Mathematicians by Gerald B. Folland Pdf

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.

Mathematical Aspects of Quantum Field Theory

Edson de Faria,Welington de Melo
Mathematical Aspects of Quantum Field Theory Book PDF

Author : Edson de Faria,Welington de Melo
Publisher : Cambridge University Press
Page : 128 pages
File Size : 52,9 Mb
Release : 2010-08-12
Category : Science
ISBN : 9781139489805

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Mathematical Aspects of Quantum Field Theory by Edson de Faria,Welington de Melo Pdf

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.

Quantum Field Theory for Mathematicians

Robin Ticciati
Quantum Field Theory for Mathematicians Book PDF

Author : Robin Ticciati
Publisher : Cambridge University Press
Page : 720 pages
File Size : 48,7 Mb
Release : 1999-06-13
Category : Mathematics
ISBN : 9780521632652

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Quantum Field Theory for Mathematicians by Robin Ticciati Pdf

This should be a useful reference for anybody with an interest in quantum theory.

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 : 43,5 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.

What Is a Quantum Field Theory?

Michel Talagrand
What Is a Quantum Field Theory Book PDF

Author : Michel Talagrand
Publisher : Cambridge University Press
Page : 759 pages
File Size : 46,5 Mb
Release : 2022-03-17
Category : Science
ISBN : 9781316510278

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What Is a Quantum Field Theory? by Michel Talagrand Pdf

A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.

Quantum Field Theory I: Basics in Mathematics and Physics

Eberhard Zeidler
Quantum Field Theory I Basics in Mathematics and Physics Book PDF

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1060 pages
File Size : 45,9 Mb
Release : 2007-04-18
Category : Science
ISBN : 9783540347644

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Quantum Field Theory I: Basics in Mathematics and Physics by Eberhard Zeidler Pdf

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Quantum Field Theory

G. B. Folland
Quantum Field Theory Book PDF

Author : G. B. Folland
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 44,6 Mb
Release : 2008-08-26
Category : Mathematics
ISBN : 9780821847053

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Quantum Field Theory by G. B. Folland Pdf

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.

From Classical Field Theory to Perturbative Quantum Field Theory

Michael Dütsch
From Classical Field Theory to Perturbative Quantum Field Theory Book PDF

Author : Michael Dütsch
Publisher : Springer
Page : 536 pages
File Size : 47,9 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783030047382

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From Classical Field Theory to Perturbative Quantum Field Theory by Michael Dütsch Pdf

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

A Prelude to Quantum Field Theory

John Donoghue,Lorenzo Sorbo
A Prelude to Quantum Field Theory Book PDF

Author : John Donoghue,Lorenzo Sorbo
Publisher : Princeton University Press
Page : 160 pages
File Size : 43,5 Mb
Release : 2022-02-22
Category : Science
ISBN : 9780691223506

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A Prelude to Quantum Field Theory by John Donoghue,Lorenzo Sorbo Pdf

A concise, beginner-friendly introduction to quantum field theory Quantum field theory is a powerful framework that extends quantum mechanics in ways that are essential in many modern applications. While it is the fundamental formalism for the study of many areas of physics, quantum field theory requires a different way of thinking, and many newcomers to the subject struggle with the transition from quantum mechanics. A Prelude to Quantum Field Theory introduces the key concepts of quantum field theory in a brief and accessible manner while never sacrificing mathematical rigor. The result is an easy-to-use textbook that distills the most general properties of the theory without overwhelming beginning students with more advanced applications. Bridges quantum mechanics and quantum field theory, emphasizing analogies and differences Emphasizes a “quantum field theoretical mindset” while maintaining mathematical rigor Obtains quantum fields as the continuum limit of a quantized system of many particles Highlights the correspondence between wave function—fundamental in quantum mechanics—and the formalism of second quantization used in quantum field theory Provides a step-by-step derivation of Feynman rules for the perturbative study of interacting theories Introduces students to renormalization, path integrals techniques, and more Discusses more modern topics like effective field theories Ideal for both undergraduate and graduate students Proven in the classroom

Mathematical Foundations of Quantum Field Theory

Albert Schwarz,Alʹbert Solomonovich Shvart︠s︡
Mathematical Foundations of Quantum Field Theory Book PDF

Author : Albert Schwarz,Alʹbert Solomonovich Shvart︠s︡
Publisher : World Scientific
Page : 383 pages
File Size : 41,7 Mb
Release : 2020
Category : Quantum field theory
ISBN : 9789813278646

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Mathematical Foundations of Quantum Field Theory by Albert Schwarz,Alʹbert Solomonovich Shvart︠s︡ Pdf

"The book is very different from other books devoted to quantum field theory, both in the style of exposition and in the choice of topics. Written for both mathematicians and physicists, the author explains the theoretical formulation with a mixture of rigorous proofs and heuristic arguments; references are given for those who are looking for more details. The author is also careful to avoid ambiguous definitions and statements that can be found in some physics textbooks. In terms of topics, almost all other books are devoted to relativistic quantum field theory, conversely this book is concentrated on the material that does not depend on the assumptions of Lorentz-invariance and/or locality. It contains also a chapter discussing application of methods of quantum field theory to statistical physics, in particular to the derivation of the diagram techniques that appear in thermo-field dynamics and Keldysh formalism. It is not assumed that the reader is familiar with quantum mechanics; the book contains a short introduction to quantum mechanics for mathematicians and an appendix devoted to some mathematical facts used in the book"--Publisher's description

Mathematical Methods of Many-Body Quantum Field Theory

Detlef Lehmann
Mathematical Methods of Many Body Quantum Field Theory Book PDF

Author : Detlef Lehmann
Publisher : CRC Press
Page : 264 pages
File Size : 40,5 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9781482286052

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Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann Pdf

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theo

An Invitation to Quantum Field Theory

Luis Alvarez-Gaumé,Miguel A. Vázquez-Mozo
An Invitation to Quantum Field Theory Book PDF

Author : Luis Alvarez-Gaumé,Miguel A. Vázquez-Mozo
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 50,9 Mb
Release : 2011-11-26
Category : Science
ISBN : 9783642237270

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An Invitation to Quantum Field Theory by Luis Alvarez-Gaumé,Miguel A. Vázquez-Mozo Pdf

This book provides an introduction to Quantum Field Theory (QFT) at an elementary level—with only special relativity, electromagnetism and quantum mechanics as prerequisites. For this fresh approach to teaching QFT, based on numerous lectures and courses given by the authors, a representative sample of topics has been selected containing some of the more innovative, challenging or subtle concepts. They are presented with a minimum of technical details, the discussion of the main ideas being more important than the presentation of the typically very technical mathematical details necessary to obtain the final results. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework.

An Introduction To Quantum Field Theory

Michael E. Peskin
An Introduction To Quantum Field Theory Book PDF

Author : Michael E. Peskin
Publisher : CRC Press
Page : 866 pages
File Size : 52,6 Mb
Release : 2018-05-04
Category : Science
ISBN : 9780429983184

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An Introduction To Quantum Field Theory by Michael E. Peskin Pdf

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Introduction to Algebraic Quantum Field Theory

S.S. Horuzhy
Introduction to Algebraic Quantum Field Theory Book PDF

Author : S.S. Horuzhy
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400911796

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Introduction to Algebraic Quantum Field Theory by S.S. Horuzhy Pdf

'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shel.f next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.