  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.
