Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators

We present the method of calculation of the radiative decays of composite quark-antiquark QQ ($) over bar systems, with different J(PC): (QQ ($) over bar)(in) -> y (QQ ($) over bar)(out). The method is relativistic invariant; it is based on the double dispersion relation integrals over the masses of the composite mesons: it can be used for high spin particles and provides us with the gauge invariant transition amplitudes. We apply this rriethod to the case when the photon is emitted by a constituent in the interinediate state (additive quark model). We perform the momentum operator expansion of the spin amplitudes for the decay processes. The problem of the nilpotent spin operators is discussed.