Geometric Mechanics: Toward a Unification of Classical Physics 2nd Edition by Richard Talman (PDF)

Description

For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately — exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. This second, fully revised edition has been expanded to include new chapters on electromagnetic theory, general relativity, and string theory. ‘Geometric Mechanics’ features illustrative examples and assumes only basic knowledge of Lagrangian mechanics.

User’s Reviews

Editorial Reviews: From the Inside Flap Mechanics is quite obviously geometric, yet the traditional approach to the subject is based mainly on differential equations. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman augments this approach with geometric methods such as differential geometry, differential forms, and tensor analysis to reveal qualitative aspects of the theory. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately – exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. This second, fully revised edition has been expanded to further emphasize the importance of the geometric approach. Starting from Hamilton’s principle, the author shows, from a geometric perspective, how “all” of classical physics can be subsumed within classical mechanics. Having developed the formalism in the context of classical mechanics, the subjects of electrodynamics, relativistic strings and general relativity are treated as examples of classical mechanics. This modest unification of classical physics is intended to provide a background for the far more ambitious “grand unification” program of quantum field theory. The final chapters develop approximate methods for the analysis of mechanical systems. Here the emphasis is more on practical perturbative methods than on the canonical transformation formalism. “Geometric Mechanics” features numerous illustrative examples and assumes only basic knowledge of Lagrangian mechanics. From the Back Cover Mechanics is quite obviously geometric, yet the traditional approach to the subject is based mainly on differential equations. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman augments this approach with geometric methods such as differential geometry, differential forms, and tensor analysis to reveal qualitative aspects of the theory. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately – exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. This second, fully revised edition has been expanded to further emphasize the importance of the geometric approach. Starting from Hamilton’s principle, the author shows, from a geometric perspective, how “all” of classical physics can be subsumed within classical mechanics. Having developed the formalism in the context of classical mechanics, the subjects of electrodynamics, relativistic strings and general relativity are treated as examples of classical mechanics. This modest unification of classical physics is intended to provide a background for the far more ambitious “grand unification” program of quantum field theory. The final chapters develop approximate methods for the analysis of mechanical systems. Here the emphasis is more on practical perturbative methods than on the canonical transformation formalism. “Geometric Mechanics” features numerous illustrative examples and assumes only basic knowledge of Lagrangian mechanics. About the Author Richard M. Talman is Professor of Physics at Cornell University, Ithaca, New York. He studied physics at the University of Western Ontario and received his Ph.D. at the California Institute of Technology in 1963. After accepting a full professorship for Physics at Cornell in 1971, he spent time as Visiting Scientist in Stanford, CERN, Berkeley, and the S.S.C. in Dallas and Saskatchewan. In addition, he has delivered lecture series at several institutions including Rice and Yale Universities. Professor Talman has been engaged in the design and construction of a series of accelerators, with special emphasis on x-rays. Read more

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