Geometric And Algebraic Topological Methods In Quantum Mechanics
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Geometric And Algebraic Topological Methods In Quantum Mechanics
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Author : Luigi Mangiarotti
language : en
Publisher: World Scientific
Release Date : 2005-01-27
Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Science categories.
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Geometric And Algebraic Topological Methods In Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2005
Geometric And Algebraic Topological Methods In Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
- The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.
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.
Geometric Algebraic And Topological Methods For Quantum Field Theory
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Author : Sylvie Payche
language : en
Publisher: World Scientific
Release Date : 2014
Geometric Algebraic And Topological Methods For Quantum Field Theory written by Sylvie Payche and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.
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.
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2013 Villa De Leyva Summer School
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Author : Alexander Cardona
language : en
Publisher: World Scientific
Release Date : 2016-09-06
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2013 Villa De Leyva Summer School written by Alexander Cardona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.
Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2011 Villa De Leyva Summer School
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Author : Sylvie Paycha
language : en
Publisher: World Scientific
Release Date : 2013-11-15
Geometric Algebraic And Topological Methods For Quantum Field Theory Proceedings Of The 2011 Villa De Leyva Summer School written by Sylvie Paycha and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-15 with Mathematics categories.
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.
Geometric And Topological Methods For Quantum Field Theory
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Author : Hernan Ocampo
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-13
Geometric And Topological Methods For Quantum Field Theory written by Hernan Ocampo 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 2005-06-13 with Science categories.
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
Geometric Formulation Of Classical And Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011
Geometric Formulation Of Classical And Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes
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Author : Maurice A De Gosson
language : en
Publisher: World Scientific
Release Date : 2017-11-10
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes written by Maurice A De Gosson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Science categories.
The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.
Topology And Geometry For Physicists
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Author : Charles Nash
language : en
Publisher: Courier Corporation
Release Date : 2013-08-16
Topology And Geometry For Physicists written by Charles Nash and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.
Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.