  The BRST generator is realized as a Hermitian nilpotent operator for a
finite-dimensional gauge system featuring a quadratic super-Hamiltonian and
linear supermomentum constraints. As a result, the emerging ordering for the
Hamiltonian constraint is not trivial, because the potential must enter the
kinetic term in order to obtain a quantization invariant under scaling. Namely,
BRST quantization does not lead to the curvature term used in the literature as
a means to get that invariance. The inclusion of the potential in the kinetic
term, far from being unnatural, is beautifully justified in light of the
Jacobi's principle.
