Quantum Topology
Quantum Topology

Author: Louis H. Kauffman

Publisher: World Scientific

Published: 1993

Total Pages: 400

ISBN-13: 9789810225759

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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.

Topology, Geometry and Quantum Field Theory
Topology, Geometry and Quantum Field Theory

Author: Ulrike Luise Tillmann

Publisher: Cambridge University Press

Published: 2004-06-28

Total Pages: 596

ISBN-13: 9780521540490

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The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

Topology And Physics - Proceedings Of The Nankai International Conference In Memory Of Xiao-song Lin
Topology And Physics - Proceedings Of The Nankai International Conference In Memory Of Xiao-song Lin

Author: Zhenghan Wang

Publisher: World Scientific

Published: 2008-08-11

Total Pages: 466

ISBN-13: 9814470651

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This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang-Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov-Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi-Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.

Differential Geometry And Physics - Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics
Differential Geometry And Physics - Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics

Author: Weiping Zhang

Publisher: World Scientific

Published: 2006-12-11

Total Pages: 542

ISBN-13: 9814476587

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This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

Quantum Computing and Quantum Communications
Quantum Computing and Quantum Communications

Author: Colin P. Williams

Publisher: Springer

Published: 2003-05-20

Total Pages: 490

ISBN-13: 3540492089

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This book contains selected papers presented at the First NASA International Conference on Quantum Computing and Quantum Communications, QCQC'98, held in Palm Springs, California, USA in February 1998. As the record of the first large-scale meeting entirely devoted to quantum computing and communications, this book is a unique survey of the state-of-the-art in the area. The 43 carefully reviewed papers are organized in topical sections on entanglement and quantum algorithms, quantum cryptography, quantum copying and quantum information theory, quantum error correction and fault-tolerant quantum computing, and embodiments of quantum computers.

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory
Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Author: Alexander Cardona

Publisher: World Scientific

Published: 2003

Total Pages: 500

ISBN-13: 9789812705068

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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.

Advances in Topological Quantum Field Theory
Advances in Topological Quantum Field Theory

Author: John M. Bryden

Publisher: Springer Science & Business Media

Published: 2007-09-27

Total Pages: 353

ISBN-13: 1402027729

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This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.

Proceedings of the Fifth International Conference on Hadronic Mechanics and Nonpotential Interactions: Physics
Proceedings of the Fifth International Conference on Hadronic Mechanics and Nonpotential Interactions: Physics

Author: Hyo Chul Myung

Publisher: Nova Publishers

Published: 1992

Total Pages: 454

ISBN-13: 9781560720430

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This volume contains the papers devoted to physics presented at the Fifth International Conference on [title] which was held at the U. of Northern Iowa in Cedar Falls, August 1990. Among the topics in 28 papers: Lie-admissible complex time model, coherent nuclear states in a supermanifold, meson-mes