  We study the action for a non-Abelian charged particle in a non-Abelian
background field in the worldline formalism, described by real bosonic
variables, leading to the well known equations given by Wong. The isospin parts
in the action can be viewed as the Lagrange multiplier term corresponding to a
non-holonomic constraint restricting the isospins to be parallel transported.
The path integration is performed over the isospin variables and as a result,
the worldlines turn out to be constrained by the classical solutions for the
isospins. We derive a wave equation from the path integral, constructed as the
constrained Hamiltonian operator acting on the wave function. The operator
ordering corresponding to the quantum Hamiltonian is found and verified by the
inverse Weyl transformation.
