  The Bakamjian-Thomas relativistic quark model, describing hadrons with a
fixed number of constituents, yields in the heavy quark limit of QCD covariant
Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules
(Bjorken-Uraltsev type sum rules). We first recall, as well as earlier results,
the new formalism presented in our recent papers on Lorentz representations,
which provide an elegant framework for the analysis of this model in the heavy
quark limit and stress the results which have been already obtained in this
direction. Then, we give some very explicit demonstrations of the fact that the
Bakamjian-Thomas framework satifies the sum rules by considering simple cases
of Isgur-Wise functions. In addition to the specific Bjorken and Uraltsev sum
rules, an important sum rule that involves only heavy mesons with light cloud
$j^P = {1 \over 2}^-$ and their radial excitations is demonstrated. This latter
sum rule is phenomenologically interesting because it constrains the
derivatives of the radially excited Isgur-Wise functions at zero recoil. On the
other hand, we recall the limitations of the Bakamjian-Thomas scheme. At finite
mass, current matrix elements with the current coupled to the heavy quark are
no longer covariant, and higher moment sum rules that hold in the heavy quark
limit of QCD are not satisfied.
