Tensor Categories And Endomorphisms Of Von Neumann Algebras
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Tensor Categories And Endomorphisms Of Von Neumann Algebras
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Author : Marcel Bischoff
language : en
Publisher: Springer
Release Date : 2015-01-13
Tensor Categories And Endomorphisms Of Von Neumann Algebras written by Marcel Bischoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-13 with Science categories.
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
Transfer Operators Endomorphisms And Measurable Partitions
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Author : Sergey Bezuglyi
language : en
Publisher: Springer
Release Date : 2018-06-21
Transfer Operators Endomorphisms And Measurable Partitions written by Sergey Bezuglyi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-21 with Mathematics categories.
The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.
Topological Phases Of Matter And Quantum Computation
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Author : Paul Bruillard
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-31
Topological Phases Of Matter And Quantum Computation written by Paul Bruillard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-31 with Education categories.
This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24–25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments. The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.
Selected Papers On Analysis And Differential Equations
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Author : American Mathematical Society
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Selected Papers On Analysis And Differential Equations written by American Mathematical Society and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."
Tensor Categories
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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05
Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Vertex Operator Algebras In Mathematics And Physics
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Vertex Operator Algebras In Mathematics And Physics written by Stephen Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
Recent Developments In Infinite Dimensional Lie Algebras And Conformal Field Theory
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Recent Developments In Infinite Dimensional Lie Algebras And Conformal Field Theory written by Stephen Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
Quantum Groups Quantum Categories And Quantum Field Theory
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Author : Jürg Fröhlich
language : en
Publisher: Springer
Release Date : 2006-11-15
Quantum Groups Quantum Categories And Quantum Field Theory written by Jürg Fröhlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Journal Of The Mathematical Society Of Japan
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Author : Nihon Sūgakkai
language : en
Publisher:
Release Date : 2007
Journal Of The Mathematical Society Of Japan written by Nihon Sūgakkai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Xivth International Congress On Mathematical Physics
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Author : Jean-claude Zambrini
language : en
Publisher: World Scientific
Release Date : 2006-03-07
Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-07 with Science categories.
In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.