On the validity of Lorentz invariance relations between parton distributions

Lorentz invariance relations connecting twist-3 parton distributions with transverse momentum dependent twist-2 distributions have been proposed previously. These relations can be extracted from a covariant decomposition of the quark-quark correlator. It is argued, however, that the derivation of the Lorentz invariance relations fails if the path-ordered exponential is taken into account in the correlator. The model independent analysis is supplemented by an explicit calculation of the corresponding parton distributions in perturbative QCD with a quark target, and in a simple spectator model. We also clarify the status of a specific calculation of time-reversal even parton distributions in light-cone gauge.