Quantization of constraint solutions
E. Kapuścik, Charles A. Uzes, A. O. Barut
The problem of connecting systems with different numbers of degrees of freedom is discussed. Constraints appropriate for ``Bose'' and ``Fermi'' quantization are used to construct algebras of Dirac brackets associated with special solutions of the nonlinear complex oscillator. The constraints are shown to provide a basis for characterizing the elementary excitations of the oscillators. An alternative notion of quantization through a correspondence with an enveloping subalgebra of the Dirac brackets is introduced, a notion which simplifies the operator-ordering problem implied by the original Dirac brackets. The infinite- and the two-dimensional representations of the subalgebra are utilized to illustrate the quantization technique.
Physical Review A•Apr 1, 1994•2 citations