One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Written in his honor, the invited papers in this volume reflect the active and vibrant research in these areas and are a tribute to Weinstein's ongoing influence. The well-recognized ...
This is the first exposition of the quantization theory of singular symplectic (i.e., Marsden-Weinstein) quotients and their applications to physics in book form. A preface by J. Marsden and A. Weinstein precedes individual refereed contributions by M.T. Benameur and V. Nistor, M. Braverman, A. Cattaneo and G. Felder, B. Fedosov, J. Huebschmann, N ...
The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of contributions to this volume cover recent advances in superstring theory, which is the leading candidate for ...
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of ...
This graduate/research level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantisation of strings, gravity and topological field theory. With chapters on random walks, random ...
This book is written by a well-known expert in classical algebraic geometry. Tyurin's research was specifically in explicit computations to vector bundles on algebraic varieties. This is the only available monograph written from his unique viewpoint. Ordinary (abelian) theta functions describe properties of moduli spaces of one-dimensional vector ...
This volume is a collection of articles by speakers at the conference "Poisson 2006: Poisson Geometry in Mathematics and Physics", which was held June 5-9, 2006, in Tokyo, Japan. Poisson 2006 was the fifth in a series of international conferences on Poisson geometry that are held once every two years. The aim of these conferences is to bring ...
The papers in this volume are based on the talks given at the conference on quantum groups dedicated to the memory of Joseph Donin, which was held at the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's distinguished mathematical career is included. Several articles, which were directly influenced by the research of Donin and ...
This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and ...
This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, ...
The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantisation of geometrical objects. The majority of contributions to this volume cover recent advances in superstring theory, which is the leading candidate for ...
This monograph deals with the geometrical and topological aspects associated with the quantization procedure, and it is shown how these features are manifested in anomaly and Berry Phase. This book is unique in its emphasis on the topological aspects of a fermion which arise as a consequence of the quantization procedure. Also, an overview of ...
This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified ...
This volume presents articles from several lectures presented at the school on 'Quantum Symmetries in Theoretical Physics and Mathematics' held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging ...
This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, ...
The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on 'Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics'. The focus is on the topics suggested by the title: Quantization in its various ...
This volume contains three extensive articles written by Karasev and his pupils. The topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate ...
This research monograph presents many new results in a rapidly developing area of great current interest. Guillemin, Ginzburg, and Karshon show that the underlying topological thread in the computation of invariants of G-manifolds is a consequence of a linearization theorem involving equivariant cobordisms. The book incorporates a novel approach ...
Recent inroads in higher-dimensional nonlinear quantum field theory and in the global theory of relevant nonlinear wave equations have been accompanied by very interesting cognate developments. These developments include symplectic quantization theory on manifolds and in group representations, the operator algebraic implementation of quantum ...
The Maslov classes have been playing an essential role in various parts of applied and pure mathematics, and physics, since the early 1970s. This volume intends to provide a thorough treatment of the Maslov classes and of their relationship with the metaplectic group. It is shown that these classes can be reconstructed, modulo 4, using only ...
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.
This graduate/research level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantisation of strings, gravity and topological field theory. With chapters on random walks, random ...
This monograph deals with the geometrical and topological aspects related to quantum field theory with special reference to the electroweak theory and skyrmions. This book is unique in its emphasis on the topological aspects of a fermion manifested through chiral anomaly which is responsible for the generation of mass. This has its relevance in ...
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