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Generalized Hamiltonian Formalism For Field Theory


Generalized Hamiltonian Formalism For Field Theory
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Generalized Hamiltonian Formalism For Field Theory


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 Hamiltonian Formalism For Field Theory Constraint Systems


Generalized Hamiltonian Formalism For Field Theory Constraint Systems
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Author : Gennadi A Sardanashvily
language : en
Publisher: World Scientific
Release Date : 1995-11-15

Generalized Hamiltonian Formalism For Field Theory Constraint Systems written by Gennadi A 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 1995-11-15 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.



New Lagrangian And Hamiltonian Methods In Field Theory


New Lagrangian And Hamiltonian Methods In Field Theory
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Author : Giovanni Giachetta
language : en
Publisher: World Scientific
Release Date : 1997-12-18

New Lagrangian And Hamiltonian Methods In Field Theory written by Giovanni 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 1997-12-18 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


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 OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo 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.



Advanced Classical 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.



Connections In Classical And Quantum Field Theory


Connections In Classical And Quantum Field Theory
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Author : L. Mangiarotti
language : en
Publisher: World Scientific
Release Date : 2000

Connections In Classical And Quantum Field Theory written by L. Mangiarotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.


Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.



Geometric Formulation Of Classical And Quantum Mechanics


Geometric Formulation Of Classical And Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011

Geometric Formulation Of Classical And Quantum Mechanics 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 2011 with Science categories.


The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.



Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory


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
Release Date : 2024-08-27

Extended Lagrange And Hamilton Formalism For Point Mechanics And Covariant Hamilton Field Theory written by Jurgen Struckmeier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-27 with Science categories.


This book presents the extended Lagrange and Hamilton formalisms of point mechanics and field theory in the usual tensor language of standard textbooks on classical dynamics. The notion 'extended' signifies that the physical time of point dynamics as well as the space-time in field theories are treated as dynamical variables. It thus elaborates on some important questions including: How do we convert the canonical formalisms of Lagrange and Hamilton that are built upon Newton's concept of an absolute time into the appropriate form of the post-Einstein era? How do we devise a Hamiltonian field theory with space-time as a dynamical variable in order to also cover General Relativity?In this book, the authors demonstrate how the canonical transformation formalism enables us to systematically devise gauge theories. With the extended canonical transformation formalism that allows to map the space-time geometry, it is possible to formulate a generalized theory of gauge transformations. For a system that is form-invariant under both a local gauge transformation of the fields and under local variations of the space-time geometry, we will find a formulation of General Relativity to emerge naturally from basic principles rather than being postulated.



Condensed Matter Field Theory


Condensed Matter Field Theory
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Author : Alexander Altland
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-11

Condensed Matter Field Theory written by Alexander Altland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-11 with Science categories.


This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.



Methods Of Differential Geometry In Classical Field Theories K Symplectic And K Cosymplectic Approaches


Methods Of Differential Geometry In Classical Field Theories K Symplectic And K Cosymplectic Approaches
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Author : Manuel De Leon
language : en
Publisher: World Scientific
Release Date : 2015-08-28

Methods Of Differential Geometry In Classical Field Theories K Symplectic And K Cosymplectic Approaches written by Manuel De Leon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-28 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.