Moyal quantization with compact symmetry groups and noncommutative harmonic analysis

The phase-space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles: covariance and traciality. This generalizes results and methods already implemented for spin systems [J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. 190, 107 (1989)]. The twisted product of phase-space functions is shown to be the image of group convolution in the context of a novel Fourier theory on the coadjoint orbits.