  The effective theory describing infinite mass particles with a given
velocity, has a great interest in heavy flavor physics. It has the unpleasant
characteristic that the energy spectrum is unbounded from below; this fact is
the source of the problems in the formulation of the euclidean theory. In this
paper we present an analysis of the euclidean effective theory, that is rather
complete and has positive conclusions. A proof of the consistency of the
euclidean theory is presented and a technique for the evaluation of the
amplitudes in perturbation theory is described. We compute also the one-loop
renormalization constants of the lattice effective theory and of the
heavy-heavy current that is needed for the determination of the Isgur-Wise
function. A variety of effects related to the explicit breaking of the Lorentz
symmetry of lattice regularization is demonstrated. The most peculiar
phenomenon is that the heavy quark velocity receives a finite renormalization.
Finally, we compute the lattice-continuum renormalization constant of the
Isgur-Wise current. It is needed for the conversion of the values of the matrix
elements computed with the lattice effective theory, to the values in the full
theory.
