Geometry, Symmetries, and Classical Physics

Geometry, Symmetries, and Classical Physics
Author :
Publisher : CRC Press
Total Pages : 702
Release :
ISBN-10 : 9781000530261
ISBN-13 : 1000530264
Rating : 4/5 (61 Downloads)

Synopsis Geometry, Symmetries, and Classical Physics by : Manousos Markoutsakis

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

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry
Author :
Publisher : Oxford University Press
Total Pages : 537
Release :
ISBN-10 : 9780199212903
ISBN-13 : 0199212902
Rating : 4/5 (03 Downloads)

Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm

A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.

Geometry, Symmetries, and Classical Physics

Geometry, Symmetries, and Classical Physics
Author :
Publisher : CRC Press
Total Pages : 482
Release :
ISBN-10 : 9781000530247
ISBN-13 : 1000530248
Rating : 4/5 (47 Downloads)

Synopsis Geometry, Symmetries, and Classical Physics by : Manousos Markoutsakis

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

Physics from Symmetry

Physics from Symmetry
Author :
Publisher : Springer
Total Pages : 294
Release :
ISBN-10 : 9783319666310
ISBN-13 : 3319666312
Rating : 4/5 (10 Downloads)

Synopsis Physics from Symmetry by : Jakob Schwichtenberg

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.

Introduction to Mechanics and Symmetry

Introduction to Mechanics and Symmetry
Author :
Publisher : Springer Science & Business Media
Total Pages : 593
Release :
ISBN-10 : 9780387217925
ISBN-13 : 0387217924
Rating : 4/5 (25 Downloads)

Synopsis Introduction to Mechanics and Symmetry by : Jerrold E. Marsden

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

The Geometry of Physics

The Geometry of Physics
Author :
Publisher : Cambridge University Press
Total Pages : 749
Release :
ISBN-10 : 9781139505611
ISBN-13 : 1139505610
Rating : 4/5 (11 Downloads)

Synopsis The Geometry of Physics by : Theodore Frankel

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

Symmetry in Mechanics

Symmetry in Mechanics
Author :
Publisher : Springer Science & Business Media
Total Pages : 201
Release :
ISBN-10 : 9781461201892
ISBN-13 : 1461201896
Rating : 4/5 (92 Downloads)

Synopsis Symmetry in Mechanics by : Stephanie Frank Singer

"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.

Geometric Formulation of Classical and Quantum Mechanics

Geometric Formulation of Classical and Quantum Mechanics
Author :
Publisher : World Scientific
Total Pages : 405
Release :
ISBN-10 : 9789814313728
ISBN-13 : 9814313726
Rating : 4/5 (28 Downloads)

Synopsis Geometric Formulation of Classical and Quantum Mechanics by : G. Giachetta

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.

Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics
Author :
Publisher : Springer Science & Business Media
Total Pages : 766
Release :
ISBN-10 : 9789400753457
ISBN-13 : 9400753454
Rating : 4/5 (57 Downloads)

Synopsis Differential Geometry and Mathematical Physics by : Gerd Rudolph

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Symmetries in Fundamental Physics

Symmetries in Fundamental Physics
Author :
Publisher : Springer
Total Pages : 806
Release :
ISBN-10 : 9783319065816
ISBN-13 : 3319065815
Rating : 4/5 (16 Downloads)

Synopsis Symmetries in Fundamental Physics by : Kurt Sundermeyer

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.