Mathematical Aspects Of Quantization
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Mathematical Aspects Of Quantization
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Author : Sam Evens
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Mathematical Aspects Of Quantization written by Sam Evens 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 2012 with Mathematics categories.
This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.
Mathematical Aspects Of Weyl Quantization And Phase
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Author : Daniel Abrom Dubin
language : en
Publisher: World Scientific
Release Date : 2000-06-12
Mathematical Aspects Of Weyl Quantization And Phase written by Daniel Abrom Dubin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-12 with Science categories.
This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.
Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups written by Paul J. Sally (Jr.) 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 1994 with Mathematics categories.
This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.
Physical And Mathematical Aspects Of Symmetries
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Author : Sergio Duarte
language : en
Publisher: Springer
Release Date : 2018-01-09
Physical And Mathematical Aspects Of Symmetries written by Sergio Duarte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-09 with Science categories.
This proceedings records the 31st International Colloquium on Group Theoretical Methods in Physics (“Group 31”). Plenary-invited articles propose new approaches to the moduli spaces in gauge theories (V. Pestun, 2016 Weyl Prize Awardee), the phenomenology of neutrinos in non-commutative space-time, the use of Hardy spaces in quantum physics, contradictions in the use of statistical methods on complex systems, and alternative models of supersymmetry. This volume’s survey articles broaden the colloquia’s scope out into Majorana neutrino behavior, the dynamics of radiating charges, statistical pattern recognition of amino acids, and a variety of applications of gauge theory, among others. This year’s proceedings further honors Bertram Kostant (2016 Wigner Medalist), as well as S.T. Ali and L. Boyle, for their life-long contributions to the math and physics communities. The aim of the ICGTMP is to provide a forum for physicists, mathematicians, and scientists of related disciplines who develop or apply methods in group theory to share their research. The 31st ICGTMP was held in Rio de Janeiro, Brazil, from June 19th to June 25th, 2016. This was the first time that a colloquium of the prestigious and traditional ICGTMP series (which started in 1972 in Marseille, France) took place in South America. (The history of the colloquia can be found at http://icgtmp.blogs.uva.es/)
The Mathematical Aspects Of Quantum Maps
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Author : Mirko Esposti
language : en
Publisher: Springer
Release Date : 2008-01-11
The Mathematical Aspects Of Quantum Maps written by Mirko Esposti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.
Mathematical Aspects Of Classical Field Theory
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Author : Mark J. Gotay
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Mathematical Aspects Of Classical Field Theory written by Mark J. Gotay 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 1992 with Science categories.
Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Mathematics Of Quantization And Quantum Fields
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Author : Jan Derezi Ski
language : en
Publisher:
Release Date : 2013-06-04
Mathematics Of Quantization And Quantum Fields written by Jan Derezi Ski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-04 with Geometric quantization categories.
A unique and definitive review of mathematical aspects of quantization and quantum field theory for graduate students and researchers.
Mathematical Aspects Of Quantum Field Theory
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Author : Edson de Faria
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Mathematical Aspects Of Quantum Field Theory written by Edson de Faria and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Science categories.
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes
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Author : Maurice A De Gosson
language : en
Publisher: World Scientific
Release Date : 2017-11-10
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes written by Maurice A De Gosson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Science categories.
The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.