QUANTIZATION OF CONSTRAINT SOLUTIONS

The problem of connecting systems with different numbers of degrees of freedom is discussed. Constraints appropriate for ''Bose'' and ''Ferm i'' quantization are used to construct algebras of Dirac brackets asso ciated with special solutions of the nonlinear complex oscillator. The constraints are shown to provide a basis for characterizing the eleme ntary excitations of the oscillators. An alternative notion of quantiz ation through a correspondence with an enveloping subalgebra of the Di rac brackets is introduced, a notion which simplifies the operator-ord ering problem implied by the original Dirac brackets. The infinite- an d the two-dimensional representations of the subalgebra are utilized t o illustrate the quantization technique.