Hermite Polynomial Representation of the Spin States

We construct the invertible map of the spin-state density operator onto the quasiprobability distribution of three continuous variables. We discuss the connection of this map with two-mode electromagnetic-field oscillators. We give the inversion formula for the spin-density matrix in terms of the Hermite polynomials. We examine the connection of the map constructed with the spin-tomographic representation. We consider the problem of the magnetic-moment rotation in the magnetic field in the suggested representation of spin states.