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.

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.

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.

Generalized Symmetries In Physics - Proceedings Of The International Symposium On Mathematical Physics
Generalized Symmetries In Physics - Proceedings Of The International Symposium On Mathematical Physics

Author: Heinz-dietrich Doebner

Publisher: World Scientific

Published: 1994-07-05

Total Pages: 446

ISBN-13: 9814550884

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This volume contains material submitted to a symposium on mathematical physics in July 1993 at the Technical University of Clausthal. It focuses on mathematical and physical notions of symmetries, especially on generalized and quantum symmetries (quantum groups and algebras) with applications to integrable systems, quasi-exact solvability, quantization methods and nonlinear problems. The workshop is a continuation of the series of meetings and workshops on mathematical physics in Clausthal which brings together mathematicians, theoretical and mathematical physicists working in the different parts of generalized symmetries. Recent developments in the mathematical structure and physical applications of generalized symmetries are discussed.

Quantum Relativity
Quantum Relativity

Author: David R. Finkelstein

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 584

ISBN-13: 3642609368

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Over the past years the author has developed a quantum language going beyond the concepts used by Bohr and Heisenberg. The simple formal algebraic language is designed to be consistent with quantum theory. It differs from natural languages in its epistemology, modal structure, logical connections, and copulatives. Starting from ideas of John von Neumann and in part also as a response to his fundamental work, the author bases his approach on what one really observes when studying quantum processes. This way the new language can be seen as a clue to a deeper understanding of the concepts of quantum physics, at the same time avoiding those paradoxes which arise when using natural languages. The work is organized didactically: The reader learns in fairly concrete form about the language and its structure as well as about its use for physics.

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.