Using a family of coherent state representations we obtain in a natural and coordinate independent wayan explicit realization of a projective unitary representation of the symplectic group. Dequantization of these operators gives us the corresponding classical functions.
Ingrid C. Daubechies, Theoretische Natuurkunde
cause the substitution has taken us out of it) is, up to some constant factor, a unitary operator. The family of these oper ators gives us our projective representation. We work with intrinsic and coordinate-free notations differing from the no tations used in Refs. 2, 3, or 4. At the end of the paper we rewrite some of the results in the more familiar x-p notations. Following the prescription given in Ref. 11 for the de quantization of these operators, we proceed then to compute the classical functions corresponding to the symplectic transformations. This calculation of classical functions for symplectic transformations has been done for one-param eter subgroups of the symplectic group.8.9 One then only
•Jan 1, 2012•0 citations