Kernel of star-product for spin tomograms

Abstract

The spin-state tomogram is presented as the modulus squared of the matrix element of the SU( 2)-group irreducible representation. For the spin system, we established explicitly a realization of the set of operators defining for spin tomograms the star-product formalism in terms of irreducible tensors. On the set of spin tomograms, the delta-function and ‘standard’ and Moyal-like kernels of the tomogram star-product are calculated explicitly in terms of Clebsch– Gordan and Racah coefficients and matrix elements of the SU( 2) irreducible representation. In the limit of infinite spin, the spin tomogram is shown to become the tomogram of the harmonic-oscillator state.