World Scientific Pubtishing, 2001, 440 pages
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Saleo, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the mode language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
Part I, Part I1 and, partially, Part I11 are intended to be a teaching proposal suitable for graduate students. Thus, they are written from the point of view of a student but with the aim of giving a general understanding of the theory. Part IV, instead, is conceed with the current research topic of completely integrable field theories and could be even used independently of the others. This part is not written with the same pedagogic spirit that animates the previous chapters and probably it would have required additional chapters conceing the Lagrangian and the Hailtonian formulation of field theory. However, a pedagogic treatment of the last subject would have taken too much space-time.
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Saleo, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the mode language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
Part I, Part I1 and, partially, Part I11 are intended to be a teaching proposal suitable for graduate students. Thus, they are written from the point of view of a student but with the aim of giving a general understanding of the theory. Part IV, instead, is conceed with the current research topic of completely integrable field theories and could be even used independently of the others. This part is not written with the same pedagogic spirit that animates the previous chapters and probably it would have required additional chapters conceing the Lagrangian and the Hailtonian formulation of field theory. However, a pedagogic treatment of the last subject would have taken too much space-time.