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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.
Book Synopsis Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) by : Gerhard Grensing
Download or read book Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) written by Gerhard Grensing and published by World Scientific. This book was released on 2021-07-15 with total page 1656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Structural Aspects of Quantum Field Theory [and Noncommutative Geometry]: Structural aspects of quantum field theory and noncommutative geometry by : Gerhard Grensing
Download or read book Structural Aspects of Quantum Field Theory [and Noncommutative Geometry]: Structural aspects of quantum field theory and noncommutative geometry written by Gerhard Grensing and published by . This book was released on 2013 with total page 1516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Structural Aspects of Quantum Field Theory [and Noncommutative Geometry]: Structural aspects of quantum field theory by : Gerhard Grensing
Download or read book Structural Aspects of Quantum Field Theory [and Noncommutative Geometry]: Structural aspects of quantum field theory written by Gerhard Grensing and published by . This book was released on 2013 with total page 1516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the 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 first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state. The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together. Errata(s) Errata (78 KB) Contents:Volume 1:Classical Relativistic Field Theory: Kinematical AspectsClassical Relativistic Field Theory: Dynamical AspectsRelativistic Quantum Field Theory: Operator MethodsNonrelativistic Quantum Mechanics: Functional Integral MethodsRelativistic Quantum Field Theory: Functional Integral MethodsQuantum Field Theory at Nonzero TemperatureVolume 2:Symmetries and Canonical FormalismGauge Symmetries and Constrained SystemsWeyl QuantizationAnomalies in Quantum Field TheoryNoncommutative GeometryQuantum GroupsNoncommutative Geometry and Quantum Groups Readership: Graduate students and professionals in theoretical and mathematical physics. Keywords:Quantum Field Theory;Quantum Groups;Noncommutative Geometry;Path Integral Techniques;Quantum Electrodynamics;Quantum ChromodynamicsReviews: “This self-contained, comprehensive first volume presents a fundamental and careful introduction to quantum field theory. It will be welcomed by students as well as researchers, since it gives an overview of the origin and development of the basic ideas of modern particle physics, quantum statistical mechanics and the mathematics behind. The book provides a rich collection of modern research topics and references to important recent published work.” Zentralblatt MATH “The publication of this authoritative and comprehensively referenced two-volume set, written in somewhat condensed but eminently lucid style and explaining the principal underlying concepts and most important results of QFT, is particularly timely and useful. I am pleased to recommend most heartily this important reference source to students and physicists and to those concerned with the philosophy of science.” George B. Kauffman Professor Emeritus of Chemistry California State University, Fresno
Book Synopsis Structural Aspects of Quantum Field Theory and Noncommutative Geometry by : Gerhard Grensing
Download or read book Structural Aspects of Quantum Field Theory and Noncommutative Geometry written by Gerhard Grensing and published by World Scientific. This book was released on 2013-05-21 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the 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 first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state. The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together. Errata(s) Errata (78 KB) Contents:Volume 1:Classical Relativistic Field Theory: Kinematical AspectsClassical Relativistic Field Theory: Dynamical AspectsRelativistic Quantum Field Theory: Operator MethodsNonrelativistic Quantum Mechanics: Functional Integral MethodsRelativistic Quantum Field Theory: Functional Integral MethodsQuantum Field Theory at Nonzero TemperatureVolume 2:Symmetries and Canonical FormalismGauge Symmetries and Constrained SystemsWeyl QuantizationAnomalies in Quantum Field TheoryNoncommutative GeometryQuantum GroupsNoncommutative Geometry and Quantum Groups Readership: Graduate students and professionals in theoretical and mathematical physics. Keywords:Quantum Field Theory;Quantum Groups;Noncommutative Geometry;Path Integral Techniques;Quantum Electrodynamics;Quantum ChromodynamicsReviews: “This self-contained, comprehensive first volume presents a fundamental and careful introduction to quantum field theory. It will be welcomed by students as well as researchers, since it gives an overview of the origin and development of the basic ideas of modern particle physics, quantum statistical mechanics and the mathematics behind. The book provides a rich collection of modern research topics and references to important recent published work.” Zentralblatt MATH “The publication of this authoritative and comprehensively referenced two-volume set, written in somewhat condensed but eminently lucid style and explaining the principal underlying concepts and most important results of QFT, is particularly timely and useful. I am pleased to recommend most heartily this important reference source to students and physicists and to those concerned with the philosophy of science.” George B. Kauffman Professor Emeritus of Chemistry California State University, Fresno
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Book Synopsis Noncommutative Geometry, Quantum Fields and Motives by : Alain Connes
Download or read book Noncommutative Geometry, Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
The Higgs boson discovery at the Large Hadron Collider in 2012 relied on boosted decision trees. Since then, high energy physics (HEP) has applied modern machine learning (ML) techniques to all stages of the data analysis pipeline, from raw data processing to statistical analysis. The unique requirements of HEP data analysis, the availability of high-quality simulators, the complexity of the data structures (which rarely are image-like), the control of uncertainties expected from scientific measurements, and the exabyte-scale datasets require the development of HEP-specific ML techniques. While these developments proceed at full speed along many paths, the nineteen reviews in this book offer a self-contained, pedagogical introduction to ML models' real-life applications in HEP, written by some of the foremost experts in their area.
Book Synopsis Artificial Intelligence For High Energy Physics by : Paolo Calafiura
Download or read book Artificial Intelligence For High Energy Physics written by Paolo Calafiura and published by World Scientific. This book was released on 2022-01-05 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Higgs boson discovery at the Large Hadron Collider in 2012 relied on boosted decision trees. Since then, high energy physics (HEP) has applied modern machine learning (ML) techniques to all stages of the data analysis pipeline, from raw data processing to statistical analysis. The unique requirements of HEP data analysis, the availability of high-quality simulators, the complexity of the data structures (which rarely are image-like), the control of uncertainties expected from scientific measurements, and the exabyte-scale datasets require the development of HEP-specific ML techniques. While these developments proceed at full speed along many paths, the nineteen reviews in this book offer a self-contained, pedagogical introduction to ML models' real-life applications in HEP, written by some of the foremost experts in their area.
Elementary particle physics is a mature subject, with a wide variety of topics. Size considerations require any text to make choices in the subject matter, and such choices are to a large extent a matter of taste. Each topic in this text has been selected for its accessibility to as wide an audience of interested readers as possible, without any compromise in mathematical sophistication. There are of necessity a lot of formulas, but every one is derived, and an effort has been made to explain the various steps and clever tricks, and how to avoid pitfalls. The text is supplemented by exercises at the end of each chapter. The reader is urged to do the exercises that are designed to increase one's skills in the material. The goal of the book is to bring to undergraduates an ability to enjoy this interesting subject.
Book Synopsis Introduction To High Energy Physics: Particle Physics For The Beginner by : Lee G Pondrom
Download or read book Introduction To High Energy Physics: Particle Physics For The Beginner written by Lee G Pondrom and published by World Scientific. This book was released on 2022-04-08 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary particle physics is a mature subject, with a wide variety of topics. Size considerations require any text to make choices in the subject matter, and such choices are to a large extent a matter of taste. Each topic in this text has been selected for its accessibility to as wide an audience of interested readers as possible, without any compromise in mathematical sophistication. There are of necessity a lot of formulas, but every one is derived, and an effort has been made to explain the various steps and clever tricks, and how to avoid pitfalls. The text is supplemented by exercises at the end of each chapter. The reader is urged to do the exercises that are designed to increase one's skills in the material. The goal of the book is to bring to undergraduates an ability to enjoy this interesting subject.
Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists. Contents:Lectures:Spectral Geometry (B Iochum)Index Theory for Non-compact G-manifolds (M Braverman and L Cano)Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods (P Aluffi)Gravitation Theory and Chern-Simons Forms (J Zanelli)Noncommutative Geometry Models for Particle Physics (M Marcolli)Noncommutative Spacetimes and Quantum Physics (A P Balachandran)Integrability and the AdS/CFT Correspondence (M Staudacher)Compactifications of String Theory and Generalized Geometry (M Graña and H Triendl)Short Communications:Groupoids and Poisson Sigma Models with Boundary (A Cattaneo and I Contreras)A Survey on Orbifold String Topology (A Angel)Grothendieck Ring Class of Banana and Flower Graphs (P Morales-Almazán)On the Geometry Underlying a Real Lie Algebra Representation (R Vargas Le-Bert) Readership: Researchers in geometry and topology, mathematical physics. Keywords:Geometry;Topology;Geometric Methods;Quantum Field Theory;Renormalization;Index Theory;Noncommutative Geometry;Quantization;String Theory;Key Features:Unique style aimed at a mixed readership of mathematicians and physicistsIdeal for self-study or use in advanced courses or seminars
Book Synopsis Geometric, Algebraic and Topological Methods for Quantum Field Theory by : Alexander Cardona
Download or read book Geometric, Algebraic and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by World Scientific. This book was released on 2013-11-15 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists. Contents:Lectures:Spectral Geometry (B Iochum)Index Theory for Non-compact G-manifolds (M Braverman and L Cano)Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods (P Aluffi)Gravitation Theory and Chern-Simons Forms (J Zanelli)Noncommutative Geometry Models for Particle Physics (M Marcolli)Noncommutative Spacetimes and Quantum Physics (A P Balachandran)Integrability and the AdS/CFT Correspondence (M Staudacher)Compactifications of String Theory and Generalized Geometry (M Graña and H Triendl)Short Communications:Groupoids and Poisson Sigma Models with Boundary (A Cattaneo and I Contreras)A Survey on Orbifold String Topology (A Angel)Grothendieck Ring Class of Banana and Flower Graphs (P Morales-Almazán)On the Geometry Underlying a Real Lie Algebra Representation (R Vargas Le-Bert) Readership: Researchers in geometry and topology, mathematical physics. Keywords:Geometry;Topology;Geometric Methods;Quantum Field Theory;Renormalization;Index Theory;Noncommutative Geometry;Quantization;String Theory;Key Features:Unique style aimed at a mixed readership of mathematicians and physicistsIdeal for self-study or use in advanced courses or seminars
This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. The main question is whether residues of Feynman integrals always evaluate to periods of mixed Tate motives, as appears to be the case from extensive computations of Feynman integrals carried out by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach grew out of work of Bloch–Esnault–Kreimer and suggests that, while the algebraic varieties associated to the Feynman graphs can be arbitrarily complicated as motives, the part that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization with those formed by mixed Tate motives. The book draws connections between these two approaches and gives an overview of various ongoing directions of research in the field. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it cal also be used by graduate students interested in working in this area.
Book Synopsis Feynman Motives by : Matilde Marcolli
Download or read book Feynman Motives written by Matilde Marcolli and published by World Scientific. This book was released on 2010 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. The main question is whether residues of Feynman integrals always evaluate to periods of mixed Tate motives, as appears to be the case from extensive computations of Feynman integrals carried out by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach grew out of work of Bloch–Esnault–Kreimer and suggests that, while the algebraic varieties associated to the Feynman graphs can be arbitrarily complicated as motives, the part that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization with those formed by mixed Tate motives. The book draws connections between these two approaches and gives an overview of various ongoing directions of research in the field. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it cal also be used by graduate students interested in working in this area.
