Introduction To Global Variational Geometry
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Introduction To Global Variational Geometry
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Introduction To Global Variational Geometry written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Introduction To Global Variational Geometry
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Introduction To Global Variational Geometry written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Lie Groups Differential Equations And Geometry
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Author : Giovanni Falcone
language : en
Publisher: Springer
Release Date : 2017-09-19
Lie Groups Differential Equations And Geometry written by Giovanni Falcone and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
Calculus Of Variations On Fibred Manifolds And Variational Physics
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Author : Jana Musilová
language : en
Publisher: Springer Nature
Release Date : 2025-02-26
Calculus Of Variations On Fibred Manifolds And Variational Physics written by Jana Musilová and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-26 with Science categories.
This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structures. The book systematically explains Lagrangian and Hamiltonian mechanics and field theory, with a focused exploration of the underlying structures. Additionally, it addresses the well-known inverse problem of calculus of variations and provides examples illustrating key variational physical theories. The text is complemented by solved examples from physics and includes exercises designed to help readers master the subject. Aimed at PhD students, postdocs, and interested researchers, this book assumes prior knowledge of mathematical analysis, linear and multilinear algebra, as well as elements of general and theoretical physics for effective engagement with the discussion.
An Introduction To Covariant Quantum Mechanics
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Author : Josef Janyška
language : en
Publisher: Springer Nature
Release Date : 2022-04-06
An Introduction To Covariant Quantum Mechanics written by Josef Janyška and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-06 with Science categories.
This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.
Noether S Theorems
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Author : Gennadi Sardanashvily
language : en
Publisher: Springer
Release Date : 2016-03-18
Noether S Theorems written by Gennadi Sardanashvily and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-18 with Mathematics categories.
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
The Inverse Problem Of The Calculus Of Variations
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Author : Dmitry V. Zenkov
language : en
Publisher: Springer
Release Date : 2015-10-15
The Inverse Problem Of The Calculus Of Variations written by Dmitry V. Zenkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-15 with Mathematics categories.
The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
The Geometry Of Ordinary Variational Equations
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Author : Olga Krupkova
language : en
Publisher: Springer
Release Date : 2006-11-14
The Geometry Of Ordinary Variational Equations written by Olga Krupkova 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.
The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.
Gauge Field Theory In Natural Geometric Language
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Author : Daniel Canarutto
language : en
Publisher:
Release Date : 2020
Gauge Field Theory In Natural Geometric Language written by Daniel Canarutto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.
Symplectic Twist Maps Global Variational Techniques
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Author : Christophe Gole
language : en
Publisher: World Scientific
Release Date : 2001-11-22
Symplectic Twist Maps Global Variational Techniques written by Christophe Gole and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-22 with Science categories.
This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.