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Geometric And Algebraic Topological Methods In Quantum Mechanics

2005-01-27 Science
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Release : 2005-01-27
Genre : Science
Kind : eBook
Book Rating : 149/5 ( reviews)

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Book Synopsis Geometric And Algebraic Topological Methods In Quantum Mechanics by : Luigi Mangiarotti

Download or read book Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti. This book was released on 2005-01-27. Available in PDF, EPUB and Kindle. Book excerpt: 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 Topological Methods for Quantum Field Theory

2010-04-29 Science
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Release : 2010-04-29
Genre : Science
Kind : eBook
Book Rating : 73X/5 ( reviews)

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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. This book was released on 2010-04-29. 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.

Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School

2016-09-06 Mathematics
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Release : 2016-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 890/5 ( reviews)

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Book Synopsis Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School by : Alexander Cardona

Download or read book Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School written by Alexander Cardona. This book was released on 2016-09-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School

2003-03-21 Mathematics
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Release : 2003-03-21
Genre : Mathematics
Kind : eBook
Book Rating : 678/5 ( reviews)

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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. This book was released on 2003-03-21. 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.

Geometric, Algebraic and Topological Methods for Quantum Field Theory

2014 Science
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Release : 2014
Genre : Science
Kind : eBook
Book Rating : 052/5 ( reviews)

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Book Synopsis Geometric, Algebraic and Topological Methods for Quantum Field Theory by : Sylvie Payche

Download or read book Geometric, Algebraic and Topological Methods for Quantum Field Theory written by Sylvie Payche. This book was released on 2014. 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.

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