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