Quantized Partial Differential Equations

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Quantized Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 2004

Quantized Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This book presents, for the first time, a systematic formulation ofthe geometric theory of noncommutative PDE''s which is suitable enoughto be used for a mathematical description of quantum dynamics andquantum field theory. A geometric theory of supersymmetric quantumPDE''s is also considered, in order to describe quantumsupergravity. Covariant and canonical quantizations of (super) PDE''sare shown to be founded on the geometric theory of PDE''s and toproduce quantum (super) PDE''s by means of functors from the categoryof commutative (super) PDE''s to the category of quantum (super)PDE''s. Global properties of solutions to (super) (commutative) PDE''sare obtained by means of their integral bordism groups.

Quantized Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 2004

Quantized Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This book presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considered, in order to describe quantum supergravity. Covariant and canonical quantizations of (super) PDE's are shown to be founded on the geometric theory of PDE's and to produce quantum (super) PDE's by means of functors from the category of commutative (super) PDE's to the category of quantum (super) PDE's. Global properties of solutions to (super) (commutative) PDE's are obtained by means of their integral bordism groups.

Quantization Nonlinear Partial Differential Equations And Operator Algebra

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Author : William Arveson
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Quantization Nonlinear Partial Differential Equations And Operator Algebra written by William Arveson 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 1996 with Mathematics categories.

This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties. Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrödinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.

Quantization Methods In The Theory Of Differential Equations

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Author : Vladimir E. Nazaikinskii
language : en
Publisher: CRC Press
Release Date : 2002-05-16

Quantization Methods In The Theory Of Differential Equations written by Vladimir E. Nazaikinskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-16 with Mathematics categories.

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 way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.

General Theory Of Partial Differential Equations And Microlocal Analysis

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Author : Min-You Qi
language : en
Publisher: CRC Press
Release Date : 1996-05-20

General Theory Of Partial Differential Equations And Microlocal Analysis written by Min-You Qi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-20 with Mathematics categories.

Quantization Pdes And Geometry

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Author : Dorothea Bahns
language : en
Publisher: Birkhäuser
Release Date : 2016-02-11

Quantization Pdes And Geometry written by Dorothea Bahns and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Differential Geometry And Its Applications International Conference

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Author : Josef Janyska
language : en
Publisher: World Scientific
Release Date : 1990-03-01

Differential Geometry And Its Applications International Conference written by Josef Janyska and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-01 with categories.

The proceedings consists of lectures and selected original research papers presented at the conference. The contents is divided into 3 parts: I. Geometric structures, II. the calculus of variations on manifolds, III. Geometric methods in physics. The volume also covers interdisciplinary areas between differential geometry and mathematical physics like field theory, relativity, classical and quantum mechanics.

Mathematical Aspects Of Weyl Quantization And Phase

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Author : Daniel Abrom Dubin
language : en
Publisher: World Scientific
Release Date : 2000-06-12

Mathematical Aspects Of Weyl Quantization And Phase written by Daniel Abrom Dubin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-12 with Science categories.

This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.

Encyclopaedia Of Mathematics Supplement Iii

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-23

Encyclopaedia Of Mathematics Supplement Iii written by Michiel Hazewinkel 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 2007-11-23 with Mathematics categories.

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Mathematics Of Quantization And Quantum Fields

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Author : Jan Dereziński
language : en
Publisher: Cambridge University Press
Release Date : 2023-02-09

Mathematics Of Quantization And Quantum Fields written by Jan Dereziński and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.

This 2013 book, now OA, offers a definitive review of mathematical aspects of quantization and quantum field theory.