Geometrical Aspects Of Quantum Fields
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Geometrical Aspects Of Quantum Fields
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Author : Andrei A. Bytsenko
language : en
Publisher: World Scientific
Release Date : 2001
Geometrical Aspects Of Quantum Fields written by Andrei A. Bytsenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
This volume presents the following topics: non-Abelian Toda models, brief remarks for physicists on equivariant cohomology and the Duistermaat-Heckman formula, Casimir effect, quantum groups and their application to nuclear physics, quantum field theory, quantum gravity and the theory of extended objects, and black hole physics and cosmology.
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes
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Author : Gerhard Grensing
language : en
Publisher: World Scientific
Release Date : 2021-07-15
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes written by Gerhard Grensing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Science categories.
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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Author : Gerhard Grensing
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry written by Gerhard Grensing and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Noncommutative function spaces categories.
'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.
Geometric And Topological Methods For Quantum Field Theory
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Author : Hernan Ocampo
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-29
Geometric And Topological Methods For Quantum Field Theory written by Hernan Ocampo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-29 with Science categories.
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.
Geometry And Quantum Field Theory
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Geometry And Quantum Field Theory written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
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 Approaches To Quantum Field Theory
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Author : Kieran Finn
language : en
Publisher: Springer Nature
Release Date : 2021-10-07
Geometric Approaches To Quantum Field Theory written by Kieran Finn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-07 with Science categories.
The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.
Aspects Of Quantum Field Theory In Curved Spacetime
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Author : Stephen A. Fulling
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-24
Aspects Of Quantum Field Theory In Curved Spacetime written by Stephen A. Fulling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-24 with Mathematics categories.
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.
Geometric Analysis And Applications To Quantum Field Theory
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Author : Peter Bouwknegt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Applications To Quantum Field Theory written by Peter Bouwknegt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Geometric And Topological Methods For Quantum Field Theory
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Author : Alexander Cardona
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-09
Geometric And Topological Methods For Quantum Field Theory written by Alexander Cardona and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Science categories.
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.
Traces In Number Theory Geometry And Quantum Fields
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Author : Sergio Albeverio
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2007-12-12
Traces In Number Theory Geometry And Quantum Fields written by Sergio Albeverio and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-12 with Mathematics categories.
Traces and determinants arise in various guises in many areas of mathematics and mathematical physics: in regularization procedures in quantum fields theory, in the definition of correlation functions and partition functions, in index theory for manifolds and for noncommutative spaces, and in the study of dynamical systems, through zeta functions and zeta determinants, as well as in number theory in the study of zeta and L-functions. This volumes shows, through a series of concrete example, specific results as well as broad overviews, how similar methods based on traces and determinants arise in different perspectives in the fields of number theory, dynamical systems, noncommutative geometry, differential geometry and quantum field theory.