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Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Author: Hisham Sati

Publisher: American Mathematical Soc.

Published: 2011-12-07

Total Pages: 370

ISBN-13: 0821851950

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Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.

Book Synopsis Mathematical Foundations of Quantum Field Theory and Perturbative String Theory by : Hisham Sati

Download or read book Mathematical Foundations of Quantum Field Theory and Perturbative String Theory written by Hisham Sati and published by American Mathematical Soc.. This book was released on 2011-12-07 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.

Quantum Fields and Strings: A Course for Mathematicians

Author: Pierre Deligne

Publisher: American Mathematical Society

Published: 1999-10-25

Total Pages: 801

ISBN-13: 0821820133

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A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Book Synopsis Quantum Fields and Strings: A Course for Mathematicians by : Pierre Deligne

Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Perturbative Algebraic Quantum Field Theory

Author: Kasia Rejzner

Publisher: Springer

Published: 2016-03-16

Total Pages: 180

ISBN-13: 3319259016

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Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Book Synopsis Perturbative Algebraic Quantum Field Theory by : Kasia Rejzner

Download or read book Perturbative Algebraic Quantum Field Theory written by Kasia Rejzner and published by Springer. This book was released on 2016-03-16 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Mathematical Aspects of Quantum Field Theories

Author: Damien Calaque

Publisher: Springer

Published: 2015-01-06

Total Pages: 572

ISBN-13: 3319099493

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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.

Book Synopsis Mathematical Aspects of Quantum Field Theories by : Damien Calaque

Download or read book Mathematical Aspects of Quantum Field Theories written by Damien Calaque and published by Springer. This book was released on 2015-01-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Non-Perturbative Foundations of Quantum Field Theory

Author: Franco Strocchi

Publisher: Oxford University Press

Published: 2013-02-14

Total Pages: 270

ISBN-13: 0199671575

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The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.

Book Synopsis An Introduction to Non-Perturbative Foundations of Quantum Field Theory by : Franco Strocchi

Download or read book An Introduction to Non-Perturbative Foundations of Quantum Field Theory written by Franco Strocchi and published by Oxford University Press. This book was released on 2013-02-14 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.

Basic Concepts of String Theory

Author: Ralph Blumenhagen

Publisher: Springer Science & Business Media

Published: 2012-10-03

Total Pages: 787

ISBN-13: 3642294979

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The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.

Book Synopsis Basic Concepts of String Theory by : Ralph Blumenhagen

Download or read book Basic Concepts of String Theory written by Ralph Blumenhagen and published by Springer Science & Business Media. This book was released on 2012-10-03 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.

Mathematical Foundations of Quantum Field Theory

Author: Albert Schwarz

Publisher: World Scientific Publishing Company

Published: 2020

Total Pages: 350

ISBN-13: 9789813278639

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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.

Book Synopsis Mathematical Foundations of Quantum Field Theory by : Albert Schwarz

Download or read book Mathematical Foundations of Quantum Field Theory written by Albert Schwarz and published by World Scientific Publishing Company. This book was released on 2020 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gravity and Strings

Author: Tomás Ortín

Publisher: Cambridge University Press

Published: 2015-03-26

Total Pages: 1043

ISBN-13: 0521768136

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Self-contained and comprehensive, this definitive new edition provides a complete overview of the intersection of gravity, supergravity, and superstrings.

Book Synopsis Gravity and Strings by : Tomás Ortín

Download or read book Gravity and Strings written by Tomás Ortín and published by Cambridge University Press. This book was released on 2015-03-26 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained and comprehensive, this definitive new edition provides a complete overview of the intersection of gravity, supergravity, and superstrings.

Advanced Topics in Quantum Field Theory

Author: M. Shifman

Publisher: Cambridge University Press

Published: 2012-01-19

Total Pages: 641

ISBN-13: 1139501887

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Since the advent of Yang–Mills theories and supersymmetry in the 1970s, quantum field theory - the basis of the modern description of physical phenomena at the fundamental level - has undergone revolutionary developments. This is the first systematic and comprehensive text devoted specifically to modern field theory, bringing readers to the cutting edge of current research. The book emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. Featuring extensive cross-referencing from traditional topics to recent breakthroughs in the field, it prepares students for independent research. The side boxes summarizing the main results and over 70 exercises make this an indispensable book for graduate students and researchers in theoretical physics.

Book Synopsis Advanced Topics in Quantum Field Theory by : M. Shifman

Download or read book Advanced Topics in Quantum Field Theory written by M. Shifman and published by Cambridge University Press. This book was released on 2012-01-19 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the advent of Yang–Mills theories and supersymmetry in the 1970s, quantum field theory - the basis of the modern description of physical phenomena at the fundamental level - has undergone revolutionary developments. This is the first systematic and comprehensive text devoted specifically to modern field theory, bringing readers to the cutting edge of current research. The book emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. Featuring extensive cross-referencing from traditional topics to recent breakthroughs in the field, it prepares students for independent research. The side boxes summarizing the main results and over 70 exercises make this an indispensable book for graduate students and researchers in theoretical physics.

Nonperturbative Quantum Field Theory

Author: G. Hooft

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 603

ISBN-13: 1461307295

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During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

Book Synopsis Nonperturbative Quantum Field Theory by : G. Hooft

Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.