Gauge transformation and constraint induced operator ordering for charged rigid planar rotator in uniform magnetic field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum p(i) (i = 1, 2, 3) in usual kinetic energy (1/2 mu) Sigma p(i)(2), and the correct kinetic energy turns out to be (1/2 mu) Sigma 1/f(i)p(i)f(i)p(i), where f(i) are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.