GROUP QUANTIZATION OF PARAMETRIZED SYSTEMS .2. PASTING HILBERT-SPACES

The method of group quantization described in the preceding paper [J. Math. Phys. 36, 4612 (1995)] is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal s urface. A simple completely solvable toy model is studied that admits a pair of maximal transversal surfaces intersecting all orbits. The co rresponding two quantum mechanics are constructed. The similarity of t he canonical group actions in the classical phase spaces on the one ha nd and in the quantum Hilbert spaces on the other hand suggests how th e two Hilbert spaces are to be pasted together. The resulting quantum theory is checked to be equivalent to that constructed directly by mea ns of Dirac's operator constraint method. The complete system of parti al Hamiltonians for any of the two transversal surfaces is chosen and the quantum Schrodinger or Heisenberg pictures of time evolution are c onstructed. (C) 1995 American Institute of Physics.