Poisson Geometry, Deformation Quantisation and Group Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poisson Geometry, Deformation Quantisation and Group Representations write by Simone Gutt. This book was released on 2005-06-21. Poisson Geometry, Deformation Quantisation and Group Representations available in PDF, EPUB and Kindle. An accessible introduction to Poisson geometry suitable for graduate students.
Deformation Quantization for Actions of $R^d$
Deformation Quantization for Actions of $R^d$ - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformation Quantization for Actions of $R^d$ write by Marc Aristide Rieffel. This book was released on 1993. Deformation Quantization for Actions of $R^d$ available in PDF, EPUB and Kindle. This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of R ]d on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.
Poisson Geometry in Mathematics and Physics
Poisson Geometry in Mathematics and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poisson Geometry in Mathematics and Physics write by Giuseppe Dito. This book was released on 2008. Poisson Geometry in Mathematics and Physics available in PDF, EPUB and Kindle. This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.
Poisson Structures
Poisson Structures - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poisson Structures write by Camille Laurent-Gengoux. This book was released on 2012-08-27. Poisson Structures available in PDF, EPUB and Kindle. Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Nonlinear Poisson Brackets
Nonlinear Poisson Brackets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Poisson Brackets write by Mikhail Vladimirovich Karasev. This book was released on 1993. Nonlinear Poisson Brackets available in PDF, EPUB and Kindle. This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
