Angular momentum, g-value, and magnetic flux of gyration states

Abstract

Two of the world's leading (Nobel laureate) physicists disagree on the definition of the orbital angular momentum L of the Landau gyration states of a spinless charged particle in a uniform external magnetic field B = B i{sub Z}. According to Richard P. Feynman (and also Frank Wilczek) L = (rx{mu}v) = rx(p - qA/c), while Felix Bloch (and also Kerson Huang) defines it as L = rxp. We show here that Bloch's definition is the correct one since it satisfies the necessary and sufficient condition LxL = i{Dirac h} L, while Feynman's definition does not. However, as a consequence of the quantized Aharonov-Bohm magnetic flux, this canonical orbital angular momentum (surprisingly enough) takes half-odd-integral values with a zero-point gyration states of L{sub Z} = {Dirac h}/2. Further, since the diamagnetic and the paramagnetic contributions to the magnetic moment are interdependent, the g-value of these gyration states is two and not one, again a surprising result for a spinless case. The differences between the gauge invariance in classical and quantum mechanics, Onsager's suggestion that the flux quantization might be an intrinsic property of the electromagnetic field-charged particle interaction, the possibility that the experimentally measured fundamental unit of the flux quantum need not necessarily imply the existence of electron pairing'' of the Bardeen-Cooper-Schrieffer superconductivity theory, and the relationship to the Dirac's angular momentum quantization condition for the magnetic monopole-charged particle composites (i.e. Schwinger's dyons), are also briefly examined from a pedestrian viewpoint.