Dirac versus Reduced Phase Space Quantization 1

The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give similar, or essentially di erent physical results, and, moreover, it is shown that there is a class of constrained systems, which can be quantized only by the Dirac method. A possible interpretation of the gauge degrees of freedom is given. Talk presented at the Geometry of Constrained Dynamical Systems Conference, Cambridge, 15-18 June 1994 On leave from the Institute for High Energy Physics, Protvino, Moscow Region, Russia; E-mail: [email protected] E-mail: [email protected]