Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes)

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Publisher : World Scientific
ISBN 13 : 9811237093
Total Pages : 1656 pages
Book Rating : 4.8/5 (112 download)

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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.

Structural Aspects of Quantum Field Theory and Noncommutative Geometry

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Publisher : World Scientific Publishing Company
ISBN 13 : 9789814472692
Total Pages : 0 pages
Book Rating : 4.4/5 (726 download)

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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 Publishing Company. This book was released on 2013 with total page 0 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.

Structural Aspects of Quantum Field Theory [and Noncommutative Geometry]: Structural aspects of quantum field theory

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Publisher :
ISBN 13 : 9789814472722
Total Pages : 1516 pages
Book Rating : 4.4/5 (727 download)

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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:

Noncommutative Structures in Mathematics and Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792369998
Total Pages : 498 pages
Book Rating : 4.3/5 (699 download)

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Book Synopsis Noncommutative Structures in Mathematics and Physics by : Steven Duplij

Download or read book Noncommutative Structures in Mathematics and Physics written by Steven Duplij and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Structural Aspects of Quantum Field Theory and Noncommutative Geometry

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Publisher : World Scientific
ISBN 13 : 9814472719
Total Pages : 1596 pages
Book Rating : 4.8/5 (144 download)

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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

Noncommutative Geometry, Quantum Fields and Motives

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Publisher : American Mathematical Soc.
ISBN 13 : 1470450453
Total Pages : 785 pages
Book Rating : 4.4/5 (74 download)

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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.

Geometry and Quantum Field Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821804006
Total Pages : 472 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.

Geometric and Topological Methods for Quantum Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 113948673X
Total Pages : 435 pages
Book Rating : 4.1/5 (394 download)

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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.

Mathematical Aspects of Quantum Field Theories

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Publisher : Springer
ISBN 13 : 3319099493
Total Pages : 572 pages
Book Rating : 4.3/5 (19 download)

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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.

Quantum Field Theory and Noncommutative Geometry

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Publisher : Springer
ISBN 13 : 3540315268
Total Pages : 0 pages
Book Rating : 4.5/5 (43 download)

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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. This book was released on 2005-04-25 with total page 0 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.

Advances in Algebraic Quantum Field Theory

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Publisher : Springer
ISBN 13 : 3319213539
Total Pages : 460 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Advances in Algebraic Quantum Field Theory by : Romeo Brunetti

Download or read book Advances in Algebraic Quantum Field Theory written by Romeo Brunetti and published by Springer. This book was released on 2015-09-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School

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Publisher : World Scientific
ISBN 13 : 9814460060
Total Pages : 378 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School by : Sylvie Paycha

Download or read book Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School written by Sylvie Paycha and published by World Scientific. This book was released on 2013-11-15 with total page 378 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.

Noncommutative Geometry, Quantum Fields and Motives

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Publisher :
ISBN 13 : 9781470432010
Total Pages : pages
Book Rating : 4.4/5 (32 download)

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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 . This book was released on 2008 with total page 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 dea.

Aspects of Quantum Field Theory in Curved Spacetime

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Publisher : Cambridge University Press
ISBN 13 : 9780521377683
Total Pages : 332 pages
Book Rating : 4.3/5 (776 download)

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Book Synopsis Aspects of Quantum Field Theory in Curved Spacetime by : Stephen A. Fulling

Download or read book Aspects of Quantum Field Theory in Curved Spacetime written by Stephen A. Fulling and published by Cambridge University Press. This book was released on 1989-08-24 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.

Quantum Spaces

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Publisher : Birkhäuser
ISBN 13 : 9783764385217
Total Pages : 0 pages
Book Rating : 4.3/5 (852 download)

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Book Synopsis Quantum Spaces by : Vincent Rivasseau

Download or read book Quantum Spaces written by Vincent Rivasseau and published by Birkhäuser. This book was released on 2007-09-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book confirms noncommutative geometry as an increasingly useful tool for the description of intricate condensed matter phenomena. It describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space. Coverage also details the very recent technique of renormalization of quantum field theories on non-commutative space-time.

Introduction to Quantum Groups

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Publisher : World Scientific
ISBN 13 : 9789810226237
Total Pages : 362 pages
Book Rating : 4.2/5 (262 download)

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Book Synopsis Introduction to Quantum Groups by : Masud Chaichian

Download or read book Introduction to Quantum Groups written by Masud Chaichian and published by World Scientific. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.

New Symmetry Principles in Quantum Field Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461534720
Total Pages : 528 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis New Symmetry Principles in Quantum Field Theory by : J. Frölich

Download or read book New Symmetry Principles in Quantum Field Theory written by J. Frölich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.