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Author: David N Yetter Publisher: World Scientific ISBN: 9814551597 Category : Languages : en Pages : 390
Book Description
This volume contains the conference on quantum topology, held at Kansas State University, Manhattan, KS, 24 - 28 March 1993.Quantum topology is a rapidly growing field of mathematics dealing with the recently discovered interactions between low-dimensional topology, the theory of quantum groups, category theory, C∗-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics. The conference, attended by over 60 mathematicians and theoretical physicists from Canada, Denmark, England, France, Japan, Poland and the United States, was highlighted by lecture series given by Louis Kauffman, Univ. of Illinois at Chicago and Nicholai Reshetikhin, Univ. of Califonia, Berkeley.
Author: David N Yetter Publisher: World Scientific ISBN: 9814551597 Category : Languages : en Pages : 390
Book Description
This volume contains the conference on quantum topology, held at Kansas State University, Manhattan, KS, 24 - 28 March 1993.Quantum topology is a rapidly growing field of mathematics dealing with the recently discovered interactions between low-dimensional topology, the theory of quantum groups, category theory, C∗-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics. The conference, attended by over 60 mathematicians and theoretical physicists from Canada, Denmark, England, France, Japan, Poland and the United States, was highlighted by lecture series given by Louis Kauffman, Univ. of Illinois at Chicago and Nicholai Reshetikhin, Univ. of Califonia, Berkeley.
Author: Louis H. Kauffman Publisher: World Scientific ISBN: 9789810225759 Category : Mathematics Languages : en Pages : 400
Book Description
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.
Author: David Ayala Publisher: American Mathematical Soc. ISBN: 1470442434 Category : Languages : en Pages : 258
Book Description
This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.
Author: Zhenghan Wang Publisher: World Scientific ISBN: 9812819118 Category : Mathematics Languages : en Pages : 466
Book Description
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 YangOCoBaxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, GromovOCoWitten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, CalabiOCoYau 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
Author: John M. Bryden Publisher: Springer Science & Business Media ISBN: 1402027729 Category : Mathematics Languages : en Pages : 353
Book Description
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.
Author: H-D Doebner Publisher: World Scientific ISBN: 9814550884 Category : Languages : en Pages : 444
Book Description
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. Contents:Representations of Quantum Groups and Their Applications:A Graph Generalization of Quantum Groups (C Gómez & G Sierra)Cross Product Quantisation, Nonabelian Cohomology and Twisting of Hopf Algebras (S Majid)Miscellaneous Physical Applications of Quantum Algebras (M Kibler)Positive Energy Representations of Noncompact Quantum Algebras (V K Dobrev)Structure of Quantum Groups and Their Differential Calculi:From Classical to Quantum: The Question of Universality (P Truini)On Quantum Groups from the Quantization Point of View (B Jurčo)Quantum Poincaré Subgroup of q-Conformal Group and q-Minkowski Geometry (M Chaichian & A P Demichev)Bicovariant Differential Calculi on Quantum Groups An-1, Bn, Cn and Dn (K Schmüdgen & A Schüler)Symmetries and Integrability:The Yang-Baxter Symmetry in Field Theory (H J de Vega)Integrable and Algebraically Solvable Systems (H-D Doebner & A G Ushveridze)Integrable Systems in Higher Dimensions (D B Fairlie)Appell Functions and the Pöschl-Teller Potential (L Lapointe & L Vinet)Symmetries in Field Theory:Can Anomalies Melt? (H Grosse et al)Renormalization of Current Algebra (J Mickelsson)Subfactors and Coset Models (K-H Rehren)Mathematical Structures:Z3-Grading and Ternary Algebraic Structures (R Kerner)Poisson Lie Groups and Nonlinear Convexity Theorems (J Hilgert K-H Neeb)Quantization on Homogeneous Compact Kähler Manifolds (D Bar-Moshe & M S Marinov)and other papers Readership: Mathematical physicists. keywords:
Author: Abhijit Champanerkar Publisher: American Mathematical Soc. ISBN: 0821849603 Category : Mathematics Languages : en Pages : 273
Book Description
This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Author: David N Yetter
Author: David N Yetter
Author: David N. Yetter
Author: David N. Yetter
Author: 
Author: Louis H. Kauffman
Author: David Ayala
Author: Zhenghan Wang
Author: John M. Bryden
Author: H-D Doebner
Author: Abhijit Champanerkar