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This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Book Synopsis A Combinatorial Perspective on Quantum Field Theory by : Karen Yeats
Download or read book A Combinatorial Perspective on Quantum Field Theory written by Karen Yeats and published by Springer. This book was released on 2016-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.
Book Synopsis Quantum Fields and Processes by : John Gough
Download or read book Quantum Fields and Processes written by John Gough and published by Cambridge University Press. This book was released on 2018-04-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.
The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Book Synopsis Combinatorial Physics by : Adrian Tanasa
Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Book Synopsis Combinatorics and Renormalization in Quantum Field Theory by : Eduardo R. Caianiello
Download or read book Combinatorics and Renormalization in Quantum Field Theory written by Eduardo R. Caianiello and published by Addison Wesley Longman. This book was released on 1973 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.
Book Synopsis Quantum Field Theory: Perspective and Prospective by : Cécile Dewitt-Morette
Download or read book Quantum Field Theory: Perspective and Prospective written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.
This volume is based upon work done by the author and his collaborators over a period of approximately twenty years and is dedicated to some selected topics of quantum field theory, which have proved of increasing importance with the passing of time.There are three parts: Combinatoric Methods Equations for Green's Functions and Perturbative Expansions Regularization, Renormalization, and Mass Equations This work will be useful to anyone interested in learning or using quantum field theory, many-body physics and, as well, to many applied mathematicians, because it introduces a number of combinatoric and analytic tools which drastically simplify, and at times bypass, treatments which customarily take up most of the bulk of the standard texts.
Book Synopsis Combinatorics And Renormalization In Quantum Field Theory by : E.r. Caianiello
Download or read book Combinatorics And Renormalization In Quantum Field Theory written by E.r. Caianiello and published by Westview Press. This book was released on 2003-04-17 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based upon work done by the author and his collaborators over a period of approximately twenty years and is dedicated to some selected topics of quantum field theory, which have proved of increasing importance with the passing of time.There are three parts: Combinatoric Methods Equations for Green's Functions and Perturbative Expansions Regularization, Renormalization, and Mass Equations This work will be useful to anyone interested in learning or using quantum field theory, many-body physics and, as well, to many applied mathematicians, because it introduces a number of combinatoric and analytic tools which drastically simplify, and at times bypass, treatments which customarily take up most of the bulk of the standard texts.
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.
This new volume takes a complete look at how classical field theory, quantum mechanics and quantum field theory are interrelated. It takes a global approach and discusses the importance of quantization by relating it to different theories such as tree amplitude and conservation laws. There arespecial chapters devoted to Euclideanization and renormalization, space and time inversion and the closed-time-path formalism.
Book Synopsis The Global Approach to Quantum Field Theory by : Bryce Seligman DeWitt
Download or read book The Global Approach to Quantum Field Theory written by Bryce Seligman DeWitt and published by Oxford University Press, USA. This book was released on 2003 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume takes a complete look at how classical field theory, quantum mechanics and quantum field theory are interrelated. It takes a global approach and discusses the importance of quantization by relating it to different theories such as tree amplitude and conservation laws. There arespecial chapters devoted to Euclideanization and renormalization, space and time inversion and the closed-time-path formalism.
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.
Book Synopsis Quantum Field Theory I: Basics in Mathematics and Physics by : Eberhard Zeidler
Download or read book Quantum Field Theory I: Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This textbook offers a detailed and uniquely self-contained presentation of quantum and gauge field theories. Writing from a modern perspective, the author begins with a discussion of advanced dynamics and special relativity before guiding students steadily through the fundamental principles of relativistic quantum mechanics and classical field theory. This foundation is then used to develop the full theoretical framework of quantum and gauge field theories. The introductory, opening half of the book allows it to be used for a variety of courses, from advanced undergraduate to graduate level, and students lacking a formal background in more elementary topics will benefit greatly from this approach. Williams provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. Worked examples are included throughout the text and end-of-chapter problems help students to reinforce key concepts. A fully worked solutions manual is available online for instructors.
Book Synopsis Introduction to Quantum Field Theory by : Anthony G. Williams
Download or read book Introduction to Quantum Field Theory written by Anthony G. Williams and published by Cambridge University Press. This book was released on 2022-07-31 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a detailed and uniquely self-contained presentation of quantum and gauge field theories. Writing from a modern perspective, the author begins with a discussion of advanced dynamics and special relativity before guiding students steadily through the fundamental principles of relativistic quantum mechanics and classical field theory. This foundation is then used to develop the full theoretical framework of quantum and gauge field theories. The introductory, opening half of the book allows it to be used for a variety of courses, from advanced undergraduate to graduate level, and students lacking a formal background in more elementary topics will benefit greatly from this approach. Williams provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. Worked examples are included throughout the text and end-of-chapter problems help students to reinforce key concepts. A fully worked solutions manual is available online for instructors.
