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Geometry of Classical Fields

Author: Ernst Binz

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 474

ISBN-13: 0486150445

A canonical quantization approach to classical field theory, this text is suitable for mathematicians interested in theoretical physics as well as to theoretical physicists who use differential geometric methods in their modelling. Introduces differential geometry, the theory of Lie groups, and progresses to discuss the systematic development of a covariant Hamiltonian formulation of field theory. 1988 edition.

Geometry, Symmetries, and Classical Physics

Author: Manousos Markoutsakis

Publisher: CRC Press

Published: 2021-12-29

Total Pages: 702

ISBN-13: 1000530264

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This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique

Geometry and Quantum Field Theory

Author: Daniel S. Freed

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 476

ISBN-13: 9780821886830

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The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Geometry of Classical Fields

Author: Ernst Binz

Publisher: North Holland

Published: 1988-01-01

Total Pages: 450

ISBN-13: 9780444705440

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This volume is an introduction to differential methods in physics. Part I contains a comprehensive presentation of the geometry of manifolds and Lie groups, including infinite dimensional settings. The differential geometric notions introduced in Part I are used in Part II to develop selected topics in field theory, from the basic principles up to the present state of the art. This second part is a systematic development of a covariant Hamiltonian formulation of field theory starting from the principle of stationary action.

Natural and Gauge Natural Formalism for Classical Field Theorie

Author: L. Fatibene

Publisher: Springer Science & Business Media

Published: 2003-11-30

Total Pages: 396

ISBN-13: 9781402017032

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In this book the authors develop and work out applications to gravity and gauge theories and their interactions with generic matter fields, including spinors in full detail. Spinor fields in particular appear to be the prototypes of truly gauge-natural objects, which are not purely gauge nor purely natural, so that they are a paradigmatic example of the intriguing relations between gauge natural geometry and physical phenomenology. In particular, the gauge natural framework for spinors is developed in this book in full detail, and it is shown to be fundamentally related to the interaction between fermions and dynamical tetrad gravity.

Methods of Differential Geometry in Classical Field Theories

Author: Manuel de León

Publisher: World Scientific

Published: 2015-10-21

Total Pages: 220

ISBN-13: 9814699772

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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

Geometry, Particles, and Fields

Author: Bjørn Felsager

Publisher:

Published: 1981

Total Pages: 668

ISBN-13:

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Teil 1: Basic properties of particles and fields. Teil 2: Basic principles and applications of differential geometry

Geometry of Classical Fields

Author: E. Binz

Publisher: Elsevier

Published: 2011-08-30

Total Pages: 447

ISBN-13: 9780080872650

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Classical Field Theory

Author: Florian Scheck

Publisher: Springer Science & Business Media

Published: 2012-05-08

Total Pages: 443

ISBN-13: 3642279856

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The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity (perihelion precession of Mercury, and light deflection by the sun). ------ Textbook features: detailed figures, worked examples, problems and solutions, boxed inserts, highlighted special topics, highlighted important math etc., helpful summaries, appendix, index.

Cubic Fields with Geometry

Author: Samuel A. Hambleton

Publisher: Springer

Published: 2018-11-07

Total Pages: 493

ISBN-13: 3030014045

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The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory. The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.