Modern interpretation of J.I. Frenkel's classical spin theory

Mathisson’s helical motions for a spinning particle: Are they unphysical?

“…The equations of motion for spinning pole-dipole particles were first derived by Mathisson [1] in the context of general relativity, though similar equations, for the case of flat spacetime, had been derived earlier by Frenkel [2] (see also [3]) in a special relativistic treatment applying to a classical model of an electron. These equations have then been further worked out and rederived most notably by Weyssenhoff-Raabe [4,5], Möller [6], Bhabha-Corben [7][8][9], Dixon [10] and Gralla et al [11], in the framework of special relativity; and in general relativity by Papapetrou [12], who carried out an exact derivation for pole-dipole particles, Tulczyjew [13], Taub [14], Dixon [15,16] and Souriau [17,18], who made derivations covariant at each step, and more recently Natário [19] and Gralla et al [20].…”

Spin-Orbital Motion and Thomas Precession in the Classical and Quantum Theories

“…The obtained in this way operator equations coincide completely in form with corresponding classical equations ath → 0, but provided the terms with the Plank constant in the latter equations should be also tended to zero (see also quasiclassical BMT approximation [12] et al). At the same time this result means that the problem of correlation between the classical and quantum Zitterbewegung remains vague.…”

“…Therefore, in the Shirokov and Frenkel formulations the spin equations coincide with the equation (21) up to terms linear in the external field. As far as the charge equation of motion are concerned they coincide with equations (11) and (12) in the linear approximations in powers ofh and in field (see also in Ref. [36], p.51).…”

“…Thereat the operator equations of motion are obtained from the Heisenberg proper time equations with the Dirac covariant Hamiltonian [12]. To found a correspondence between the classical and quantum equations of motion it is necessary to separate out the terms responsible for quantum Zitterbewegung.…”

“…Later the Bargmann-Michel-Telegdi (BMT) classical spin equation [6] in accordance with the Frenkel spin equation (see [7]) was obtained on the basis of the relativistic quasiclassical spin theory [8,[9][10][11] and the Heisenberg equations of operators motion in the relativistic quantum mechanics (see [12]). After that the situation has changed.…”