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Partial Algebras And Their Operator Realizations

Author: J-P Antoine
Publisher: Springer Science & Business Media
ISBN: 9401700656
Size: 14.27 MB
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Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmüdgen [1990] and A. Inoue [1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).

Contemporary Problems In Mathematical Physics

Author: Jan Govaerts
Publisher: World Scientific
ISBN: 981448184X
Size: 33.55 MB
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The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their physics applications can be conceived, developed and disseminated. Basic ideas for addressing a variety of contemporary problems in mathematical and theoretical physics are presented in a nonintimidating atmosphere. Experts provide the reader the fundamentals to predict new possibilities in physics and other fields. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Diffeomorphisms Groups in Quantum Physics (G A Goldin)On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field Theory (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:A Stochastic Streamflow Model Based on a Minimum Energy Expenditure Concept (A Afouda et al.)Regge Poles Trajectories for Nonsingular Potentials: The Thomas-Fermi Potentials (Z Felfli et al.)Proposed Differential Equation for Spin 1/2 (H V Mweene)Influence of Diseases and Arterial Prostheses on Solitary Blood Waves: Characteristics of an Ideal Prosthesis (S Noubissié & P Woafo)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Vector Coherent States over Matrix Domains (S T Ali)Wavelet Analysis and Some of Its Applications in Physics (J-P Antoine)Some Variations on the Berezin Quantization Method (M Engliš)Variational Analysis, PDE's and Image Analysis: The Big Picture and a Sampling of Details (N D George & K R Vixie)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Orthogonal Polynomials of Class One (E S Azatassou & M N Hounkonnou)and other papers Readership: Researchers and professionals in physics and mathematics. Keywords:Mathematical Physics;Theoretical Physics;Quantum Physics;Coherent States;Supersymmetry

Two Dimensional Conformal Geometry And Vertex Operator Algebras

Author: Yi-Zhi Huang
Publisher: Springer Science & Business Media
ISBN: 1461242762
Size: 14.62 MB
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The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

A Panorama Of Modern Operator Theory And Related Topics

Author: Harry Dym
Publisher: Springer Science & Business Media
ISBN: 3034802218
Size: 15.62 MB
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This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.