  Gauge theories with general covariance are particularly reluctant to
quantization. We discuss the example of the Hamiltonian formulation of the
relativistic point particle that, despite its apparent simplicity, is of
crucial importance since a number of point particle systems can be cast into
this form on a higher dimensional Rindler background, as recently pointed out
by Hojman. It is shown that this system can be equipped with a hidden local,
symmetry generating, constraint which on the one hand does not bother the
classical evolution and on the other hand simplifies the realization of the
path integral quantization. Even though the positive impact of the hidden
symmetry is more evident in the Lagrangian version of the theory, it is still
present through the suggested Hamiltonian constraint.
