Introduction to Symplectic Dirac Operators

Author: Katharina Habermann,Lutz Habermann

Publisher: Springer

ISBN: 3540334211

Category: Mathematics

Page: 125

View: 7174

This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
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Geometric Methods in Physics

XXXI Workshop, Białowieża, Poland, June 24–30, 2012

Author: Piotr Kielanowski,S. Twareque Ali,Alexander Odesskii,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov

Publisher: Springer Science & Business Media

ISBN: 3034806450

Category: Mathematics

Page: 237

View: 307

The Białowieża workshops on Geometric Methods in Physics, taking place in the unique environment of the Białowieża natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938–2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.​
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Twenty Years of Bialowieza: A Mathematical Anthology

Aspects of Differential Geometric Methods in Physics

Author: S Twareque Ali,Gerard G Emch,Anatol Odzijewicz,Martin Schlichenmaier,Stanislaw L Woronowicz

Publisher: World Scientific

ISBN: 9814481033

Category: Science

Page: 276

View: 1255

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. Contents:Aspects of Quantization:Diffeomorphism Groups and Quantum Configurations (G A Goldin)Functorial Quantization and the Guillemin–Sternberg Conjecture (N P Landsman)Coherent State Method in Geometric Quantization (A Odzijewicz)The Group of Volume Preserving Diffeomorphisms and the Lie Algebra of Unimodular Vector Fields: Survey of Some Classical and Not-So-Classical Results (C Roger)Symplectic and Poisson Geometry:Moduli Space of Germs of Symplectic Connections of Ricci Type (M Cahen)Banach Lie–Poisson Spaces (A Odzijewicz & T S Ratiu)Other Mathematical Methods:Spectra of Operators Associated with Dynamical Systems: From Ergodicity to the Duality Principle (A B Antonevich et al.)An Ergodic Arnold-Liouville Theorem for Locally Symmetric Spaces (J Hilgert)The Renormalization Fixed Point as a Mathematical Object (R P Langlands)A Cohomological Description of Abelian Bundles and Gerbes (R Picken)On a Quantum Group of Unitary Operators: The Quantum az + b Group (W Pusz & S L Woronowicz) Readership: Physicists and mathematicians in the area of differential geometric methods in physics. Keywords:Quantization;Symplectic Geometry;Coherent States;Diffeomorphism Groups;Quantum Groups;Ergodicity;Renormalization;Symmetric SpacesKey Features:This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in PhysicsThe articles collected here are written by leading experts in the field
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A Course in Algebra

Author: Ėrnest Borisovich Vinberg

Publisher: American Mathematical Soc.

ISBN: 9780821834138

Category: Mathematics

Page: 511

View: 1872

This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook.Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.
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Geometric Methods for Quantum Field Theory

Author: Hernan Ocampo,Sylvie Paycha,Andres Reyes

Publisher: World Scientific

ISBN: 9814492825

Category: Science

Page: 528

View: 5355

Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg–Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents:Lectures:Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher)Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi)Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann)Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski)Renormalized Traces as a Geometric Tool (S Paycha)Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun)An Introduction to Seiberg-Witten Theory (H Ocampo)Short Communications:Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona)Multiplicative Anomaly for the ς-Regularized Determinant (C Ducourtioux)On Cohomogeneity One Riemannian Manifolds (S M B Kashani)A Differentiable Calculus on the Space of Loops and Connections (M Reiris)Quantum Hall Conductivity and Topological Invariants (A Reyes)Determinant of the Dirac Operator Over the Interval [0,β] (F Torres-Ardila) Readership: Mathematicians and physicists. Keywords:Reviews:“Many texts in theoretical physics do not contain a rigorous account of the mathematics they employ. However, this text does, and it omits no steps in the logic, thus making it very accessible to the mathematical community. Also it emphasizes physics, providing a link between the two disciplines which one rarely finds in a text.”Contemporary Physics
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Dirac-Operatoren in der Riemannschen Geometrie

Mit einem Ausblick auf die Seiberg-Witten-Theorie

Author: Thomas Friedrich

Publisher: Springer-Verlag

ISBN: 3322803023

Category: Mathematics

Page: 207

View: 7683

Dieses Buch entstand nach einer einsemestrigen Vorlesung an der Humboldt-Universität Berlin im Studienjahr 1996/ 97 und ist eine Einführung in die Theorie der Spinoren und Dirac-Operatoren über Riemannschen Mannigfaltigkeiten. Vom Leser werden nur die grundlegenden Kenntnisse der Algebra und Geometrie im Umfang von zwei bis drei Jahren eines Mathematik- oder Physikstudiums erwartet. Ein Anhang gibt eine Einführung in das aktuelle Gebiet der Seiberg-Witten-Theorie.
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An Introduction to Noncommutative Geometry

Author: Joseph C. Várilly

Publisher: European Mathematical Society

ISBN: 9783037190241

Category: Mathematics

Page: 113

View: 4664

Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.
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Veröffentlichungen

Author: GENERALVERWALTUNG DER MAX-PLANCK-GESELLSCHAFT (München).,Max-Planck-Gesellschaft zur Förderung der Wissenschaften,Sigrid Deutschmann

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 6601

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Einführung in die Mechanik und Symmetrie

Eine grundlegende Darstellung klassischer mechanischer Systeme

Author: Jerrold E. Marsden,Tudor S. Ratiu

Publisher: Springer-Verlag

ISBN: 3642568599

Category: Mathematics

Page: 598

View: 4552

Symmetrie spielt in der Mechanik eine große Rolle. Dieses Buch beschreibt die Entwicklung zugrunde liegender Theorien. Besonderes Gewicht wird der Symmetrie beigemessen. Ursache hierfür sind Entwicklungen im Bereich dynamischer Systeme, der Einsatz geometrischer Verfahren und neue Anwendungen. Dieses Lehrbuch stellt Grundlagen bereit und beschreibt zahlreiche spezifische Anwendungen. Interessant für Physiker und Ingenieure. Ausgewählte Beispiele, Anwendungen, aktuelle Verfahren/Techniken veranschaulichen die Theorie.
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Differentialgeometrie, Topologie und Physik

Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 5538

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.
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L'Enseignement mathématique

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6296

Vols. for 1965- include a separately paged section, Bulletin bibliographique.
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Classical and Quantum Dynamics of Constrained Hamiltonian Systems

Author: Heinz J. Rothe,Klaus Dieter Rothe

Publisher: World Scientific

ISBN: 9814299650

Category: Mathematics

Page: 316

View: 4019

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
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Group Theory

Author: Helmut Wielandt

Publisher: Walter de Gruyter

ISBN: 3110863383

Category: Mathematics

Page: 821

View: 5169

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