Groups Invariants Integrals And Mathematical Physics
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Groups Invariants Integrals And Mathematical Physics
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Author : Maria Ulan
language : en
Publisher: Springer Nature
Release Date : 2023-05-31
Groups Invariants Integrals And Mathematical Physics written by Maria Ulan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Science categories.
This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.
Golden Age Of Theoretical Physics The Boxed Set Of 2 Vols
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Author : Jagdish Mehra
language : en
Publisher: World Scientific
Release Date : 2001-02-28
Golden Age Of Theoretical Physics The Boxed Set Of 2 Vols written by Jagdish Mehra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-28 with Science categories.
The Golden Age of Theoretical Physics brings together 37 selected essays. Many of these essays were first presented as lectures at various universities in Europe and the USA, and then published as reports or articles. Their enlarged, final versions were published in the joint work of Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, while the other essays were published as articles in scientific journals or in edited books. Here they are published together as a tribute to the Mehra-Rechenberg collaboration sustained for several decades, and cover various aspects of quantum theory, the special and general theories of relativity, the foundations of statistical mechanics, and some of their fundamental applications. Two essays, ‘Albert Einstein's “First” Paper’ (Essay 1) and ‘The Dream of Leonardo da Vinci’ (Essay 37), lie outside the major themes treated in this book, but are included here because of their historical interest. The origin of each essay is explained in a footnote.This book deals with the most important themes developed in the first 40 years of the twentieth century by some of the greatest pioneers and architects of modern physics. It is a vital source of information about what can veritably be described as ‘the golden age of theoretical physics’.
Applications Of Lie Groups To Difference Equations
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Author : Vladimir Dorodnitsyn
language : en
Publisher: CRC Press
Release Date : 2010-12-01
Applications Of Lie Groups To Difference Equations written by Vladimir Dorodnitsyn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.
Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods
The Feynman Integral And Feynman S Operational Calculus
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Author : Gerald W. Johnson
language : en
Publisher: Clarendon Press
Release Date : 2000-03-16
The Feynman Integral And Feynman S Operational Calculus written by Gerald W. Johnson and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
Group Theoretic Methods In Mechanics And Applied Mathematics
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Author : D.M. Klimov
language : en
Publisher: CRC Press
Release Date : 2014-04-21
Group Theoretic Methods In Mechanics And Applied Mathematics written by D.M. Klimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-21 with Mathematics categories.
Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.
Quantum Invariants
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Author : Tomotada Ohtsuki
language : en
Publisher: World Scientific
Release Date : 2002
Quantum Invariants written by Tomotada Ohtsuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.
Differential Geometry Differential Equations And Mathematical Physics
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Author : Maria Ulan
language : en
Publisher: Springer Nature
Release Date : 2021-02-12
Differential Geometry Differential Equations And Mathematical Physics written by Maria Ulan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-12 with Mathematics categories.
This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.
Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer Nature
Release Date : 2024-05-27
Knots And Primes written by Masanori Morishita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-27 with Mathematics categories.
This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory. After an informative introduction to Gauss' work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original. References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry. This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.
Library Of Congress Subject Headings
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Author : Library of Congress. Cataloging Policy and Support Office
language : en
Publisher:
Release Date : 2007
Library Of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Subject headings, Library of Congress categories.
Library Of Congress Subject Headings
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Author : Library of Congress
language : en
Publisher:
Release Date : 2004
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Subject headings, Library of Congress categories.