Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-30
Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by Maurice A. de Gosson 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 2011-07-30 with Mathematics categories.
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Author :
language : en
Publisher: Springer
Release Date : 2012-02-05
Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-05 with categories.
Quantum Harmonic Analysis
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Author : Maurice A. de Gosson
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-07-05
Quantum Harmonic Analysis written by Maurice A. de Gosson and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Mathematics categories.
Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Harmonic Analysis And Partial Differential Equations
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Author : Justin Feuto
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
Harmonic Analysis And Partial Differential Equations written by Justin Feuto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
This proceedings volume collects selected papers presented at the Harmonic Analysis and Applications Workshop held in Abidjan, Côte d'Ivoire from May 22-26, 2023. Chapters present surveys and recent research results from experts and cover a range of topics at the intersections of classical and abstract harmonic analysis, PDEs, and numerical analysis.
Advances In Microlocal And Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-03-03
Advances In Microlocal And Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-03 with Mathematics categories.
The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Born Jordan Quantization
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Author : Maurice A. de Gosson
language : en
Publisher: Springer
Release Date : 2016-01-11
Born Jordan Quantization written by Maurice A. de Gosson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-11 with Science categories.
This book presents a comprehensive mathematical study of the operators behind the Born–Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.
Quantum Versus Classical Mechanics And Integrability Problems
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Author : Maciej Błaszak
language : en
Publisher: Springer
Release Date : 2019-06-11
Quantum Versus Classical Mechanics And Integrability Problems written by Maciej Błaszak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Science categories.
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Infinite Dimensional Analysis Quantum Probability And Applications
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Author : Luigi Accardi
language : en
Publisher: Springer Nature
Release Date : 2022-10-04
Infinite Dimensional Analysis Quantum Probability And Applications written by Luigi Accardi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-04 with Mathematics categories.
This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.
Landscapes Of Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Landscapes Of Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory Modulation space theory Applications to the medical industry Wavelet transform theory Anti-Wick operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Numerical Computations Theory And Algorithms
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Author : Yaroslav D. Sergeyev
language : en
Publisher: Springer Nature
Release Date : 2024-12-31
Numerical Computations Theory And Algorithms written by Yaroslav D. Sergeyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Computers categories.
The three-volume set LNCS 14476-14478 constitutes the post conference proceedings of the 4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023, held in Pizzo Calabro, Italy, during June 14-20, 2023. The 45 full papers presented in this book together with 60 short papers were carefully reviewed and selected from 170 submissions. The papers focus on topics such as: continuous and discrete single- and multi-objective problems, local, global and large-scale optimization, classification in machine learning, optimal control, and applications; computational and applied mathematics (such as approximation theory, computational geometry, computational fluid dynamics, dynamical systems and differential equations, numerical algebra, etc.) and applications in engineering and science; numerical models, methods and software using traditional and emerging high-performance computational tools and paradigms (including the infinity and quantum computing) and their application in artificial intelligence and data science, bioinformatics, economics and management, engineering and technology, mathematical education, number theory and foundations of mathematics, etc.