  In Dirac's canonical quantization theory on systems with second-class
constraints, the commutators between the position, momentum and Hamiltonian
form a set of algebraic relations that are fundamental in construction of both
the quantum momentum and the Hamiltonian. For a free particle on a
two-dimensional sphere or a spherical top, results show that the well-known
canonical momentum p_{{\theta}} breaks one of the relations, while three
components of the momentum expressed in the three-dimensional Cartesian system
of axes as p_{i} (i=1,2,3) are satisfactory all around. This momentum is not
only geometrically invariant but also self-adjoint, and we call it geometric
momentum. The nontrivial commutators between p_{i} generate three components of
the orbital angular momentum; thus the geometric momentum is fundamental to the
angular one. We note that there are five different forms of the geometric
momentum proposed in the current literature, but only one of them turns out to
be meaningful.
