Classical and Quantum Dynamics of Constrained Hamiltonian Systems

Devoted to the study of the classical and quantum dynamics of physics theories where the Lagrangian exhibits local (gauge) symmetries, the purpose of this text is to both introduce this field of constrained dynamical systems and provide tools for quantizing such systems. The authors (both of the U. Heidelberg, Germany) first present the classical treatment in chapters that address the local (gauge) symmetry systems as singular Lagrangian systems, the classical Hamiltonian formulation based on the work of Dirac, the symplectic approach for handling singular systems, second class systems where quantization poses some problems resolvable by gauge theory, and the Hamilton-Jacoby formulation of the classical dynamics of constrained systems. They then explore the problem of quantizing systems with first and second class constraints, addressing purely second class systems which allow an operator quantization based on equations of motion formulated using the notion of an extended Hamiltonian, quantization of second class systems using functional methods, and the functional quantization of first class systems in dynamical gauges. Annotation c2010 Book News, Inc., Portland, OR (booknews.com)