  The relations existing between the auxiliary field (einbein field) formalism
and the spinless Salpeter equation are studied in the case of two particles
with the same mass, interacting via a confining potential. The problem of
non-orthogonality for radial excited states in the auxiliary field formalism is
discussed and found to be non-crucial. It is shown that the classical equations
of motion of the rotating string model, derived from the QCD lagrangian, reduce
exactly to the classical equations of motion of the phenomenological
semirelativistic flux tube model, provided all auxiliary fields are eliminated
correctly from the rotating string hamiltonian.
