Reduction in systems with local symmetry

This review is devoted to problems associated with the study of dynamical s ystems with a finite number of degrees of freedom possessing local symmetry . The procedure of reduction of the system of dynamical equations to the no rmal form, where the Cauchy problem has a unique solution, is discussed wit hin the framework of the classical Lagrangian and Hamiltonian theory. Speci al attention is given to the geometrical reduction scheme, which allows the physical subspace in the phase space of a degenerate dynamical system to b e distinguished, and makes it possible to find the explicit form of the cor responding canonical variables without introducing additional gauge-fixing conditions (gauges) into the theory. The two reduction procedures, the geom etrical method and the gauge-fixing method, are compared in order to unders tand what conditions on the gauges guarantee the correctness of the reducti on procedure. (C) 1999 American Institute of Physics. [S1063-7796(99)00401- 5].