Transformations in the angle–angular-momentum phase space

Squeezing transformations in the discrete ${\mathit{Z}}_{2\mathit{j}+1\mathrm{}}$×${\mathit{Z}}_{2\mathit{j}+1\mathrm{}}$ angle–angular-momentum phase space are shown to be associated with the SL(2,${\mathit{Z}}_{2\mathit{j}+1\mathrm{}}$) group and important special cases are explicitly constructed. ‘‘Spherical’’ bases are introduced in the direct sum of all the Hilbert spaces ${\mathit{H}}_{2\mathit{j}+1\mathrm{}}$ and the corresponding representations are defined. Transformations of these bases, using area preserving diffeomorphisms on a sphere, are studied and potential applications in quantum-optics models are discussed.