Quantization And Infinite Dimensional Systems

Author : S.T. Ali,J-P Antoine,W. Lisiecki,I.M. Mladenov,A. Odzijewicz
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781461525646

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Quantization and Infinite-Dimensional Systems by S.T. Ali,J-P Antoine,W. Lisiecki,I.M. Mladenov,A. Odzijewicz Pdf

As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day.

Author : J-P Antoine,S.T. Ali,W. Lisiecki,I.M. Mladenov,Anatol Odzijewicz
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489910608

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Quantization, Coherent States, and Complex Structures by J-P Antoine,S.T. Ali,W. Lisiecki,I.M. Mladenov,Anatol Odzijewicz Pdf

The XIIIth Bialowieza Summer Workshop was held from July 9 to 15, 1994. While still within the general framework of Differential Geometric Methods in Physics, the XnIth Workshop was expanded in scope to include quantum groups, q-deformations and non-commutative geometry. It is expected that lectures on these topics will now become an integral part of future workshops. In the more traditional areas, lectures were devoted to topics in quantization, field theory, group representations, coherent states, complex and Poisson structures, the Berry phase, graded contractions and some infinite-dimensional systems. Those of us who have taken part in the evolution of the workshops over the years, feel a good measure of satisfaction with the excellent quality of the papers presented, in particular the mathematical rigour and novelty. Each year a significant number of new results are presented and future directions of research are discussed. Their freshness and immediacy inevitably leads to intense discussions and an exchange of ideas in an informal and physically charming environment. The present workshop also had a higher attendance than its predecessors, with ap proximately 65 registered participants. As usual, there was a large number of graduate students and young researchers among them.

Author : B. Grigelionis,Yu. V. Prohorov,V. V. Sazonov,V. Statulevičius
Publisher : Walter de Gruyter GmbH & Co KG
Page : 624 pages
File Size : 55,7 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112319024

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Probability Theory and Mathematical Statistics. Vol. 2 by B. Grigelionis,Yu. V. Prohorov,V. V. Sazonov,V. Statulevičius Pdf

No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 53,5 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

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Quantum Theory, Groups and Representations by Peter Woit Pdf

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Author : Jan Govaerts,M Norbert Hounkonnou,Alfred Z Msezane
Publisher : World Scientific
Page : 504 pages
File Size : 42,9 Mb
Release : 2002-10-18
Category : Science
ISBN : 9789814488686

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Contemporary Problems in Mathematical Physics by Jan Govaerts,M Norbert Hounkonnou,Alfred Z Msezane Pdf

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. Contents:Quantization Techniques: A Quick Overview (S T Ali)The Quantum Geometer's Universe: Particles, Interactions and Topology (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:Do Cross-Sections Determine Phase Shifts Uniquely? (D Atkinson)Hilbert Transform or Kramers-Kronig Relations Applied to Some Aspects of Linear and Nonlinear Physics (G Debiais)Application of the Gibbs Sampler to the Conditional Simulation of Rain Fields (H Onibon et al.)The Mathematics of an Algebraic Approach to the Physics of Hadrons (M D Slaughter)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Phase Space Geometry in Classical and Quantum Mechanics (J R Klauder)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One (E Azatassou & M N Hounkonnou)On a Generalization of the Method by Barbaroux et al. for the Improvement on the Rate of Decay of an Operator Resolvent (G Honnouvo & M N Hounkonnou)and other papers Readership: Researchers in mathematical physics, theoretical physics, physical chemistry, analysis and differential equations, atomic and quantum physics. Keywords:

Author : S Twareque Ali,Anatol Odzijewicz,I M Mladenov
Publisher : World Scientific
Page : 256 pages
File Size : 53,8 Mb
Release : 1993-10-29
Category : Electronic
ISBN : 9789814522038

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Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics by S Twareque Ali,Anatol Odzijewicz,I M Mladenov Pdf

The aim of the conference was to find common elements between quantization and coherent states, and quantization on Poisson manifolds. Topics included are coherent states, geometric quantization, phase space quantization, deformation and *-products and Berry's phase.

Author : Michel Talagrand
Publisher : Cambridge University Press
Page : 759 pages
File Size : 47,7 Mb
Release : 2022-03-17
Category : Science
ISBN : 9781316510278

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What Is a Quantum Field Theory? by Michel Talagrand Pdf

A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.

Author : Pascal Auscher,T. Coulhon,Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 52,8 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821833834

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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by Pascal Auscher,T. Coulhon,Alexander Grigoryan Pdf

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Author : George W. Mackey
Publisher : Courier Corporation
Page : 162 pages
File Size : 52,6 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9780486154473

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Mathematical Foundations of Quantum Mechanics by George W. Mackey Pdf

This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.

Author : Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau
Publisher : Springer
Page : 347 pages
File Size : 41,8 Mb
Release : 2018-06-01
Category : Science
ISBN : 9783319767321

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Coherent States and Their Applications by Jean-Pierre Antoine,Fabio Bagarello,Jean-Pierre Gazeau Pdf

Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814464666

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Mathematical Horizons for Quantum Physics by Anonim Pdf

Author : Ladislav Šamaj,Zoltán Bajnok
Publisher : Cambridge University Press
Page : 525 pages
File Size : 51,9 Mb
Release : 2013-05-16
Category : Science
ISBN : 9781107067660

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Introduction to the Statistical Physics of Integrable Many-body Systems by Ladislav Šamaj,Zoltán Bajnok Pdf

Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

Author : S Twareque Ali,Gerard Gustav Emch,Anatol Odzijewicz,Martin Schlichenmaire,Stanislaw L Woronowicz
Publisher : World Scientific
Page : 275 pages
File Size : 54,7 Mb
Release : 2005-01-27
Category : Science
ISBN : 9789814481038

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Twenty Years Of Bialowieza: A Mathematical Anthology: Aspects Of Differential Geometric Methods In Physics by S Twareque Ali,Gerard Gustav Emch,Anatol Odzijewicz,Martin Schlichenmaire,Stanislaw L Woronowicz Pdf

This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1-7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience.This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view.

Author : Aleksandr Aleksandrovich Kirillov
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 40,6 Mb
Release : 2004
Category : Lie groups
ISBN : 9780821835302

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Lectures on the Orbit Method by Aleksandr Aleksandrovich Kirillov Pdf

Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Author : A.K. Prykarpatsky,I.V. Mykytiuk
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 44,9 Mb
Release : 2013-04-09
Category : Science
ISBN : 9789401149945

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,I.V. Mykytiuk Pdf

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).