Abstract
With the aid of a covariant spin formalism, the kinematic constraint equations for helicity amplitudes are studied in a systematic way for all mass configurations, including the case of zero-mass particles. The complete set of constraints at thresholds and pseudothresholds is given in a form convenient for calculation; that is, the coefficients of the helicity amplitudes are simple numerical ones (as opposed, for instance, to $D$ functions). For nonzero-mass particles, the reduction of the constraints in terms of total spin amplitudes is shown to follow. Amplitudes with different values of total spin are not related at thresholds or pseudo-thresholds.
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