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Starting from the general formulation of current matrix elements in theBakamjian-Thomas (BT) approach to quark models, certain aspects of their heavyquark limit are exhibited in an intuitive form, allowing a common treatment forany number of quarks and angular momenta j,j'. We use the general Falkinterpretation of Isgur-Wise functions as overlaps of light parton states inmotion. Then, in BT, for small collinear velocities, the motion of these statesis described by a very simple dimensionless differential operator O acting onthe internal wave functions of the light quarks, which is a relativisticgeneralisation of the dipole operator times the quark mass : it appears as thegenerator of Lorentz transformations for N free light particles.

Simple operator formulation of the Bakamjian-Thomas approach to heavy  quark current , with generalisation to HQET, and with applications to  transitions of Lambda-b