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Loop Spaces, Characteristic Classes and Geometric Quantization

2009-12-30 Mathematics
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Release : 2009-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 317/5 ( reviews)

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Book Synopsis Loop Spaces, Characteristic Classes and Geometric Quantization by : Jean-Luc Brylinski

Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski. This book was released on 2009-12-30. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.

Quantum Topology

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 759/5 ( reviews)

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Book Synopsis Quantum Topology by : Louis H. Kauffman

Download or read book Quantum Topology written by Louis H. Kauffman. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

Integrable Systems, Topology, and Physics

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 394/5 ( reviews)

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Book Synopsis Integrable Systems, Topology, and Physics by : Martin A. Guest

Download or read book Integrable Systems, Topology, and Physics written by Martin A. Guest. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations--all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference also available from the AMS is Differential Geometry and Integrable Systems, Volume 308 CONM/308 in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.

Symplectic Geometry and Quantization

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 026/5 ( reviews)

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Book Synopsis Symplectic Geometry and Quantization by : Yoshiaki Maeda

Download or read book Symplectic Geometry and Quantization written by Yoshiaki Maeda. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a state-of-the-art discussion of recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants.

Lie Theory and Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 612/5 ( reviews)

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Book Synopsis Lie Theory and Geometry by : Jean-Luc Brylinski

Download or read book Lie Theory and Geometry written by Jean-Luc Brylinski. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant’s work.

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