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Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes
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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 (In 2 Volumes) by : Gerhard Grensing
Download or read book Structural Aspects Of Quantum Field Theory (In 2 Volumes) 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: 'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis 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.
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:
Author :Ursula Carow-Watamura Publisher :Springer Science & Business Media ISBN 13 :9783540239000 Total Pages :316 pages Book Rating :4.2/5 (39 download)
Book Synopsis Quantum Field Theory and Noncommutative Geometry by : Ursula Carow-Watamura
Download or read book Quantum Field Theory and Noncommutative Geometry written by Ursula Carow-Watamura and published by Springer Science & Business Media. This book was released on 2005-02-21 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
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.
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.
Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona
Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
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.
Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by Cambridge University Press. This book was released on 2010-04-29 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 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.
Book Synopsis Geometry, Topology and Quantum Field Theory by : P. Bandyopadhyay
Download or read book Geometry, Topology and Quantum Field Theory written by P. Bandyopadhyay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap.
Book Synopsis Quantum Gravity by : Bertfried Fauser
Download or read book Quantum Gravity written by Bertfried Fauser and published by Springer Science & Business Media. This book was released on 2007-02-15 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. The contributions have been strictly refereed and are written in an accessible style. The present volume emerged from the 2nd Blaubeuren Workshop "Mathematical and Physical Aspects of Quantum Gravity".
Book Synopsis Noncommutative Spacetimes by : Paolo Aschieri
Download or read book Noncommutative Spacetimes written by Paolo Aschieri and published by Springer. This book was released on 2009-07-07 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.
Book Synopsis Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School by : Alexander Cardona
Download or read book Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School written by Alexander Cardona and published by World Scientific. This book was released on 2003-03-21 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.
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.
Book Synopsis Noncommutative Geometry And Physics 4 - Workshop On Strings, Membranes And Topological Field Theory by : Yoshiaki Maeda
Download or read book Noncommutative Geometry And Physics 4 - Workshop On Strings, Membranes And Topological Field Theory written by Yoshiaki Maeda and published by World Scientific. This book was released on 2017-03-16 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the lectures and talks presented in the Tohoku Forum for Creativity in the thematic year 2015 'Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information', and related events in the period 2014-2016.This volume especially contains an overview of recent developments in the theory of strings and membranes, as well as topological field theory.
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