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.
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 w
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.
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.
Quantization Nonlinear Partial Differential Equations And Operator Algebra
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Author : John Von Neumann
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Quantization Nonlinear Partial Differential Equations And Operator Algebra written by John Von Neumann 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 Science categories.
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 dynamics, and differential geometric, general relativistic, and purely algebraic aspects. Quantization and Nonlinear Wave Equations thus was highly appropriate as the theme for the first John von Neumann Symposium (June 1994) held at MIT. The symposium was intended to treat topics of emerging signifigance underlying future mathematical developments. 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 Schrodinger 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.
Non Linear Partial Differential Operators And Quantization Procedures
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Author : S.I. Andersson
language : en
Publisher: Springer
Release Date : 2006-11-14
Non Linear Partial Differential Operators And Quantization Procedures written by S.I. Andersson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Pseudo Differential Operators
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Author : Hans G. Feichtinger
language : en
Publisher: Springer
Release Date : 2008-08-15
Pseudo Differential Operators written by Hans G. Feichtinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-15 with Mathematics categories.
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
Non Linear Partial Differential Operators And Quantization Procedures
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Author : S. I. Andersson
language : en
Publisher:
Release Date : 1983
Non Linear Partial Differential Operators And Quantization Procedures written by S. I. Andersson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Pseudo Differential Operators
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Author : Hans G. Feichtinger
language : en
Publisher: Springer
Release Date : 2009-08-29
Pseudo Differential Operators written by Hans G. Feichtinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
The Quantization Of Gravity
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Author : Claus Gerhardt
language : en
Publisher: Springer
Release Date : 2018-04-14
The Quantization Of Gravity written by Claus Gerhardt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-14 with Science categories.
A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.