Generalized Hamiltonian Formalism For Field Theory Constraint Systems
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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.
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.
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.
Geometrical Dynamics Of Complex Systems
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Author : Vladimir G. Ivancevic
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
Geometrical Dynamics Of Complex Systems written by Vladimir G. Ivancevic 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 2006-09-10 with Science categories.
Geometrical Dynamics of Complex Systems is a graduate?level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By?complexsystems?,inthis book are meant high?dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:engineering,physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi?input multi?output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular ?soft complexity philosophy?, we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high?dimensional nonlinear systems and processes of ?real life? can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well?known that linear systems, which are completely predictable and controllable by de?nition ? live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
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.
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. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. 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.
Quantum Field Theory
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Author : Anthony G. Williams
language : en
Publisher: Cambridge University Press
Release Date : 2022-08-04
Quantum Field Theory written by Anthony G. Williams 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 2022-08-04 with Science categories.
This textbook offers a detailed and self-contained presentation of quantum field theory, suitable for advanced undergraduate and graduate level courses. The author provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. A fully worked solutions manual is available online for instructors.
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems
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Author : Heinz J. Rothe
language : en
Publisher: World Scientific
Release Date : 2010
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems written by Heinz J. Rothe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
Gauge Mechanics
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Author : L. Mangiarotti
language : en
Publisher: World Scientific
Release Date : 1998
Gauge Mechanics 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 1998 with Science categories.
This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.
40 Years In Mathematical Physics
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Author : L. D. Faddeev
language : en
Publisher: World Scientific
Release Date : 1995
40 Years In Mathematical Physics written by L. D. Faddeev 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.
This is a collection of Prof L D Faddeev's important lectures, papers and talks. Some of these have not been published before and some have, for the first time, been translated from Russian into English. The topics covered correspond to several distinctive and pioneering contributions of Prof Faddeev to modern mathematical physics: quantization of Yang?Mills and Einstein gravitational fields, soliton theory, the many-dimensional inverse problem in potential scattering, the Hamiltonian approach to anomalies, and the theory of quantum integrable models. There are also two papers on more general aspects of the interrelations between physics and mathematics as well as an autobiographical essay.