Texts and Readings in Physical Sciences

Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. The authors of this book treat classical dynamics as a subject in its own right as well as a research frontier. Incorporating insights gained over the past several decades, they present the essential principles of classical dynamics and demonstrate that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.

Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion of constrained systems, and on Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory.

This reprinting of Sudarshan and Mukunda's Classical Dynamics: A Modern Perspective is faithful to the original text in letter and in spirit. It is a testimony to the vitality of the book that the point of view it offers has remained relevant over nearly half a century.

1 Introduction: Newtonian Mechanics
2 Generalized Coordinates and Lagrange's Equations
3 The Hamilton and Weiss Variational Principles and the Hamilton Equations of Motion
4 The Relation Between the Lagrangian and the Hamiltonian Descriptions
5 Invariance Properties of the Lagrangian & Hamiltonian Descriptions, Poisson and Lagrange Brackets, and Canonical Transformations
6 Group Properties and Methods of Constructing Canonical Transformations
7 Invariant Measures in Phase Space and Various Forms of Development in Time
8 Theory of Systems with Constraints
9 The Generalized Poisson Bracket and Its Applications
10 Dynamical Systems with Infinitely Many Degrees of Freedom and Theory of Fields
11 Linear and Angular Momentum Dynamical Variables and Their Significance
12 Sets, Topological Spaces, Groups
13 Lie Groups and Lie Algebras
14 Realizations of Lie Groups and Lie Algebras
15 Some Important Lie Groups and Their Lie Algebras
16 Relativistic Symmetry in the Hamiltonian Formalism
17 The Three-Dimensional Rotation Group
18 The Three-Dimensional Euclidean Group
19 The Galilei Group
20 The Poincare Group
21 Manifest Covariance in Hamiltonian Mechanics
22 Relativistic Action-at-a-Distance Theories
23 Conclusion
Index