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We present the method of calculation of radiative decays of compositequark-antiquark systems with different J^{PC}: (Q\bar Q)_{in} -> gamma (Q\barQ)_{out}. The method is relativistic invariant, it is based on the doubledispersion relation integrals over the masses of composite mesons, it can beused for the high spin particles and provides us with the gauge invarianttransition amplitudes. We apply this method to the case when the photon isemitted by a constituent in the intermediate state (additive quark model). Weperform the momentum operator expansion of the spin amplitudes for the decayprocesses. The problem of nilpotent spin operators is discussed.Comment: 21 pages, 1 figur

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