Generalized Hamiltonian Formalism For Field Theory
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Generalized Hamiltonian Formalism For Field Theory
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Author : G. Sardanashvily
language : en
Publisher: World Scientific
Release Date : 1995
Generalized Hamiltonian Formalism For Field Theory written by G. Sardanashvily and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.
Generalized Classical Mechanics And Field Theory
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Author : M. de León
language : en
Publisher: Elsevier
Release Date : 2011-08-30
Generalized Classical Mechanics And Field Theory written by M. de León and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Science categories.
The aim of this book is to discuss the present situation of Lagrangian and Hamiltonian formalisms involving higher order derivatives. The achievements of differential geometry in formulating a more modern and powerful treatment of these theories is described and an extensive review of the development of these theories in classical language is also given.
Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory
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Author : Jurgen Struckmeier
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-05-31
Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory written by Jurgen Struckmeier and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-31 with Science categories.
This book offers an explicitly covariant canonical formalism that is devised in the usual mathematical language of standard textbooks on classical dynamics. It elaborates on important questions: How do we convert the entire canonical formalism of Lagrange and Hamilton that are built upon Newton's concept of an absolute time into a relativistically correct form that is appropriate to our present knowledge? How do we treat the space-time variables in a Hamiltonian Field Theory on equal footing as in the Lagrangian description of field theory without introducing a new mathematical language? How can a closed covariant canonical gauge theory be obtained from it? To answer the last question, the theory of homogenous and inhomogeneous gauge transformations is worked out in this book on the basis of the canonical transformation theory for fields elaborated before. In analogy to the treatment of time in relativistic point mechanics, the canonical formalism in field theory is further extended to a space-time that is no longer fixed but is also treated as a canonical variable. Applied to a generalized theory of gauge transformations, this opens the door to a new approach to general relativity.
New Lagrangian And Hamiltonian Methods In Field Theory
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 1997
New Lagrangian And Hamiltonian Methods In Field Theory written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Science categories.
This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.
Advanced Classical Field Theory
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2009
Advanced Classical Field Theory written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Science categories.
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories ? gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory ? are presented in a complete way.This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.
Hamiltonian Field Theory In The Radiating Regime
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Author : Piotr T. Chrusciel
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-12-04
Hamiltonian Field Theory In The Radiating Regime written by Piotr T. Chrusciel 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 2001-12-04 with Science categories.
The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.
Advanced Classical Field Theory
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Author :
language : en
Publisher:
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Advanced Classical Field Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Methods Of Differential Geometry In Classical Field Theories
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Author : Manuel de León
language : en
Publisher: World Scientific
Release Date : 2015-10-21
Methods Of Differential Geometry In Classical Field Theories written by Manuel de León and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-21 with Mathematics categories.
This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism. It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject. Contents:A Review of Hamiltonian and Lagrangian Mechanics:Hamiltonian and Lagrangian Mechanicsk-Symplectic Formulation of Classical Field Theories:k-Symplectic Geometryk-Symplectic FormalismHamiltonian Classical Field TheoryHamilton–Jacobi Theory in k-Symplectic Field TheoriesLagrangian Classical Field TheoriesExamplesk-Cosymplectic Formulation of Classical Field Theories:k-Cosymplectic Geometryk-Cosymplectic FormalismHamiltonian Classical Field TheoriesHamilton–Jacobi EquationLagrangian Classical Field TheoriesExamplesk-Symplectic Systems versus Autonomous k-Cosymplectic SystemsRelationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:Multisymplectic FormalismAppendices:Symplectic ManifoldsCosymplectic ManifoldsGlossary of Symbols Readership: Graduate students and researchers in classical field theories. Key Features:This book contains for the first time this new geometric approach to Classical Field Theory. Up to now the theory is disseminated in several journal papersThe subject is very active in the last yearsThere are many open problems in Classical Field Theories to be attacked using this new formalismKeywords:Classical Field Theory;k-Symplectic;k-Cosymplectic;Multisymplectic Formalism
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.
Mathematical Foundations Of Quantum Field Theory
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Author : Albert Schwarz
language : en
Publisher: World Scientific
Release Date : 2020
Mathematical Foundations Of Quantum Field Theory written by Albert Schwarz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Quantum field theory categories.
"The book is very different from other books devoted to quantum field theory, both in the style of exposition and in the choice of topics. Written for both mathematicians and physicists, the author explains the theoretical formulation with a mixture of rigorous proofs and heuristic arguments; references are given for those who are looking for more details. The author is also careful to avoid ambiguous definitions and statements that can be found in some physics textbooks. In terms of topics, almost all other books are devoted to relativistic quantum field theory, conversely this book is concentrated on the material that does not depend on the assumptions of Lorentz-invariance and/or locality. It contains also a chapter discussing application of methods of quantum field theory to statistical physics, in particular to the derivation of the diagram techniques that appear in thermo-field dynamics and Keldysh formalism. It is not assumed that the reader is familiar with quantum mechanics; the book contains a short introduction to quantum mechanics for mathematicians and an appendix devoted to some mathematical facts used in the book"--Publisher's description