$C^*$-Algebras: 1943-1993
Author:
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 434
ISBN-13: 0821851756
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C*-algebras
Author: Robert S. Doran
Publisher: American Mathematical Soc.
Published: 1994-01-01
Total Pages: 436
ISBN-13: 9780821855041
DOWNLOAD EBOOKThe book contains carefully written expository and research articles by leaders in the field, including a reprint of the original 1943 paper on C[* algebras by Gelfand and Neumark.
C*-Algebras
Author: Joachim Cuntz
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 281
ISBN-13: 364257288X
DOWNLOAD EBOOKThis book contains a collection of articles provided by the participants of the SFB-workshop on C*-algebras, March 8 - March 12, 1999 which was held at the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the University of Münster, Germany. The aim of the workshop was to bring together leading experts in the theory of C* -algebras with promising young researchers in the field, and to provide a stimulating atmosphere for discussions and interactions between the participants. There were 19 one-hour lectures on various topics like - classification of nuclear C* -algebras, - general K-theory for C* -algebras, - exact C* -algebras and exact groups, - C*-algebras associated to (infinite) matrices and C*-correspondences, - noncommutative prob ability theory, - deformation quantization, - group C* -algebras and the Baum-Connes conjecture, giving a broad overview of the latest developments in the field, and serving as a basis for discussions. We, the organizers of the workshop, were greatly pleased with the excellence of the lectures and so were led to the idea of publishing the proceedings of the conference. There are basically two kinds of contributions. On one side there are several articles giving surveys and overviews on new developments and im portant results of the theory, on the other side one finds original articles with interesting new results.
Operator Theory
Author: Barry Simon
Publisher: American Mathematical Soc.
Published: 2015-12-04
Total Pages: 769
ISBN-13: 1470411032
DOWNLOAD EBOOKA Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.
Elements of Noncommutative Geometry
Author: Jose M. Gracia-Bondia
Publisher: Springer Science & Business Media
Published: 2013-11-27
Total Pages: 692
ISBN-13: 1461200059
DOWNLOAD EBOOKNew Spaces in Physics
Author: Mathieu Anel
Publisher: Cambridge University Press
Published: 2021-04
Total Pages: 437
ISBN-13: 110849062X
DOWNLOAD EBOOKIn this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.
Mathematical Topics Between Classical and Quantum Mechanics
Author: Nicholas P. Landsman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 547
ISBN-13: 146121680X
DOWNLOAD EBOOKThis monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.
Photons In Fock Space And Beyond (In 3 Volumes)
Author: Reinhard Honegger
Publisher: World Scientific
Published: 2015-04-22
Total Pages: 2353
ISBN-13: 9814618853
DOWNLOAD EBOOKThe three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.
Around Langlands Correspondences
Author: Farrell Brumley
Publisher: American Mathematical Soc.
Published: 2017
Total Pages: 394
ISBN-13: 147043573X
DOWNLOAD EBOOKPresents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
L2-Invariants: Theory and Applications to Geometry and K-Theory
Author: Wolfgang Lück
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 604
ISBN-13: 3662046873
DOWNLOAD EBOOKIn algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
