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This book provides an
innovative and
mathematically sound treatment of the foundations of analytical
mechanics and the relation of classical mechanics to relativity and
quantum theory. It is intended for use at the introductory graduate
level.
A distinguishing feature
of the book
is its integration of special relativity into the teaching of
classical mechanics. After a thorough review of the traditional
theory, Part II of the book introduces extended Lagrangian and
Hamiltonian methods that treat time as a transformable coordinate
rather than the fixed parameter of Newtonian physics. Advanced
topics such as covariant Lagrangians and Hamiltonians, canonical
transformations, and Hamilton-Jacobi methods are simplified by the
use of this extended theory. And the definition of canonical
transformation no longer excludes the Lorentz transformation of
special relativity.
This is also a book for
those who
study analytical mechanics to prepare for a critical exploration of
quantum mechanics. Comparisons to quantum mechanics appear
throughout the text. The extended Hamiltonian theory with time as a
coordinate is compared to Dirac's formalism of primary phase space
constraints. The chapter on relativistic mechanics shows how to use
covariant Hamiltonian theory to write the Klein-Gordon and Dirac
equations. The chapter on Hamilton-Jacobi theory includes a
discussion of the closely related Bohm hidden variable model of
quantum mechanics. Classical mechanics itself is presented with an
emphasis on methods, such as linear vector operators and dyadics,
that will familiarize the student with similar techniques in quantum
theory.
Graduate students
preparing for
research careers will find a graduate mechanics course based on this
book to be an essential bridge between their undergraduate training
and advanced study in analytical mechanics, relativity, and quantum
mechanics.
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