Topology And Quantum Theory In Interaction
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Topology And Quantum Theory In Interaction
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Author : David Ayala
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-25
Topology And Quantum Theory In Interaction written by David Ayala 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 2018-10-25 with Mathematics categories.
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.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed 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 2019-08-23 with Mathematics categories.
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Contact Interactions In Quantum Mechanics Theory Mathematical Aspects And Applications
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Author : Manuel Gadella
language : en
Publisher: Frontiers Media SA
Release Date : 2021-03-12
Contact Interactions In Quantum Mechanics Theory Mathematical Aspects And Applications written by Manuel Gadella and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-12 with Science categories.
Topological Aspects Of Condensed Matter Physics
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Author : Claudio Chamon
language : en
Publisher: Oxford University Press
Release Date : 2017
Topological Aspects Of Condensed Matter Physics written by Claudio Chamon and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Science categories.
This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.
Strongly Interacting Quantum Systems Out Of Equilibrium
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Author : Thierry Giamarchi
language : en
Publisher: Oxford University Press
Release Date : 2016
Strongly Interacting Quantum Systems Out Of Equilibrium written by Thierry Giamarchi and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.
This book presents new experimental tools and theoretical concepts of collective nonequilibrium behavior of quantum systems. The book is based on the Les Houches Summer School of August 2012, "Strongly interacting quantum systems out of equilibrium".
Intermolecular Interactions In Crystals
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Author : Juan J Novoa
language : en
Publisher: Royal Society of Chemistry
Release Date : 2017-10-25
Intermolecular Interactions In Crystals written by Juan J Novoa and has been published by Royal Society of Chemistry this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-25 with Science categories.
The field of crystal engineering concerns the design and synthesis of molecular crystals with desired properties. This requires an in-depth understanding of the intermolecular interactions within crystal structures. This new book brings together the latest information and theories about intermolecular bonding, providing an introductory text for graduates. The book is divided into three parts. The first part covers the nature, physical meaning and methods for identification and analysis of intermolecular bonds. The second part explains the different types of bond known to occur in molecular crystals, with each chapter written by a specialist in that specific bond type. The final part discusses the cooperativity effects of different bond types present in one solid. This comprehensive textbook will provide a valuable resource for all students and researchers in the field of crystallography, materials science and supramolecular chemistry.
Integrability From Statistical Systems To Gauge Theory
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Author : Patrick Dorey
language : en
Publisher:
Release Date : 2019
Integrability From Statistical Systems To Gauge Theory written by Patrick Dorey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
This volume contains lectures delivered at the Les Houches Summer School 'Integrability: from statistical systems to gauge theory' held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.
Geometry And Physics
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Author : H. Pedersen
language : en
Publisher: CRC Press
Release Date : 2021-01-08
Geometry And Physics written by H. Pedersen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-08 with Mathematics categories.
"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."
Fundamental Problems In Statistical Mechanics Viii
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Author : H. Van Beijeren
language : en
Publisher: Elsevier
Release Date : 2016-04-20
Fundamental Problems In Statistical Mechanics Viii written by H. Van Beijeren and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Science categories.
In keeping with the tradition of previous summer schools on fundamental problems in statistical mechanics, this book contains in depth treatemnts of topics of current interest in statistical mechanics and closely related fields. The topics covered include: dynamical impurity problems, quantum phase transitions, vortex liquids and glasses, quasicrystals and related aperiodic structures, pattern formation, turbulence, exactly solvable models, polymers, phase transitions in colloids, interfaces and two-dimensional gravity.
Proceedings Of The Second International Workshop On Contemporary Problems In Mathematical Physics
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Author : Jan Govaerts
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The Second International Workshop On Contemporary Problems In Mathematical Physics written by Jan Govaerts and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.