Quantization Of Singular Symplectic Quotients

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Quantization Of Singular Symplectic Quotients

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Author : N.P. Landsman
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Quantization Of Singular Symplectic Quotients written by N.P. Landsman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Quantization Of Singular Symplectic Quotients

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Author : Nicholas P. Landsman
language : en
Publisher: Birkhauser
Release Date : 2001-01-01

Quantization Of Singular Symplectic Quotients written by Nicholas P. Landsman and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.

Kahler Spaces Nilpotent Orbits And Singular Reduction

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Author : Johannes Huebschmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Kahler Spaces Nilpotent Orbits And Singular Reduction written by Johannes Huebschmann 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 2004 with Mathematics categories.

For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.

Kontsevich S Deformation Quantization And Quantum Field Theory

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Author : Nima Moshayedi
language : en
Publisher: Springer Nature
Release Date : 2022-08-11

Kontsevich S Deformation Quantization And Quantum Field Theory written by Nima Moshayedi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-11 with Mathematics categories.

This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder. This subject originated from an attempt to understand the mathematical structure when passing from a commutative classical algebra of observables to a non-commutative quantum algebra of observables. Developing deformation quantization as a semi-classical limit of the expectation value for a certain observable with respect to a special sigma model, the book carefully describes the relationship between the involved algebraic and field-theoretic methods. The connection to quantum field theory leads to the study of important new field theories and to insights in other parts of mathematics such as symplectic and Poisson geometry, and integrable systems. Based on lectures given by the author at the University of Zurich, the book will be of interest to graduate students in mathematics or theoretical physics. Readers will be able to begin the first chapter after a basic course in Analysis, Linear Algebra and Topology, and references are provided for more advanced prerequisites.

Galois Theory Hopf Algebras And Semiabelian Categories

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Author : George Janelidze
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Galois Theory Hopf Algebras And Semiabelian Categories written by George Janelidze 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 2004 with Mathematics categories.

This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabeliancategories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers,specifically those interested in Galois theory and Hopf algebras and their categorical unification.

Singularity Theory Dedicated To Jean Paul Brasselet On His 60th Birthday Proceedings Of The 2005 Marseille Singularity School And Conference

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Author : Jean-paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007-02-08

Singularity Theory Dedicated To Jean Paul Brasselet On His 60th Birthday Proceedings Of The 2005 Marseille Singularity School And Conference written by Jean-paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-08 with Mathematics categories.

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Coxeter Matroids

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Author : Alexandre V. Borovik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Coxeter Matroids written by Alexandre V. Borovik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained text provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of matroids which is based on a finite Coxeter group. Key topics and features: * Systematic, clearly written exposition with ample references to current research * Matroids are examined in terms of symmetric and finite reflection groups * Finite reflection groups and Coxeter groups are developed from scratch * The Gelfand-Serganova theorem is presented, allowing for a geometric interpretation of matroids and Coxeter matroids as convex polytopes with certain symmetry properties * Matroid representations in buildings and combinatorial flag varieties are studied in the final chapter * Many exercises throughout * Excellent bibliography and index Accessible to graduate students and research mathematicians alike, "Coxeter Matroids" can be used as an introductory survey, a graduate course text, or a reference volume.

Momentum Maps And Hamiltonian Reduction

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Author : Juan-Pablo Ortega
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Momentum Maps And Hamiltonian Reduction written by Juan-Pablo Ortega and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

The use of the symmetries of a physical system in the study of its dynamics has a long history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques are often implemented by using the integrals 01 motion that one can sometimes associate to these symmetries. The integrals of motion of a dynamical system are quan tities that are conserved along the fiow of that system. In c1assieal mechanics symme tries are usually induced by point transformations, that is, they come exc1usively from symmetries of the configuration space; the intimate connection between integrals of motion and symmetries was formalized in this context by NOETHER (1918). This idea can be generalized to many symmetries of the entire phase space of a given system, by associating to the Lie algebra action encoding the symmetry, a function from the phase space to the dual of the Lie algebra. This map, whose level sets are preserved by the dynamics of any symmetrie system, is referred to in modern terms as a momentum map of the symmetry, a construction already present in the work of LIE (1890). Its remarkable properties were rediscovered by KOSTANT (1965) and SOURlAU (1966, 1969) in the general case and by SMALE (1970) for the lifted action to the co tangent bundle of a configuration space. For the his tory of the momentum map we refer to WEINSTEIN (1983b) and MARSDEN AND RATIU (1999), §11. 2.

Lie Groups Beyond An Introduction

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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-21

Lie Groups Beyond An Introduction written by Anthony W. Knapp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-21 with Mathematics categories.

This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.

Rigid Analytic Geometry And Its Applications

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Author : Jean Fresnel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Rigid Analytic Geometry And Its Applications written by Jean Fresnel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.