Download or read book Generalized Hamiltonian Formalism for Field Theory written by G. Sardanashvily and published by World Scientific. This book was released on 1995 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Classical Mechanics and Field Theory written by M. de León and published by Elsevier. This book was released on 2011-08-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory written by Jurgen Struckmeier and published by World Scientific Publishing Company. This book was released on 2017-05-31 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book New Lagrangian and Hamiltonian Methods in Field Theory written by G. Giachetta and published by World Scientific. This book was released on 1997 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Classical and Quantum Dynamics of Constrained Hamiltonian Systems written by Heinz J. Rothe and published by World Scientific. This book was released on 2010 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. All topics are well illustrated with examples emphasizing points of central interest. The book should enable graduate students to follow the literature on this subject without much problems, and to perform research in this field.
Download or read book Connections in Classical and Quantum Field Theory written by L Mangiarotti and published by World Scientific. This book was released on 2000-04-28 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. keywords:Lagrangian Field Theory;Hamiltonian Field Theory;Classical Mechanics;BRST Formalism;Topological Field Theories;Non-Commutative Geometry;Theoretical Physics;Mathematical Physics;Fibre Bundle;Connection;Jet Manifold;Gauge Theory;Gravitation;Theory;Quantum Field;Geometric Quantization;Supergeometry;BRST;Theory “this book certainly offers a valuable supplement to the existing literature on the impact of connection theory on theoretical physics.” Mathematical Reviews
Download or read book A Student s Guide to Lagrangians and Hamiltonians written by Patrick Hamill and published by Cambridge University Press. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Download or read book Advanced Classical Field Theory written by G. Giachetta and published by World Scientific. This book was released on 2009 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamiltonian Field Theory in the Radiating Regime written by Piotr T. Chrusciel and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Methods of Differential Geometry in Classical Field Theories written by Manuel de León and published by World Scientific. This book was released on 2015-10-21 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Advanced Classical Field Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Noether s Theorems written by Gennadi Sardanashvily and published by Springer. This book was released on 2016-03-18 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Classical Field Theory written by G. Giachetta and published by World Scientific. This book was released on 2009 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Download or read book Connections in Classical and Quantum Field Theory written by L. Mangiarotti and published by World Scientific. This book was released on 2000 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Principles in Classical Mechanics written by Douglas Cline and published by . This book was released on 2018-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.
