THE QUANTIZATION OF THE CLASSICAL THEORY OF SPINNING PARTICLES

Abstract

The classical theory of particles, possessing charge and dipole moment, and moving in an electromagnetic field, is considered on the assumptions that there is no constraint connection between the rotational variables and the velocity of the particle, and that the two invariant squares of the dipole moment six–vector are constants of the motion. Two different schemes are obtained according as the two invariant scalar products of the dipole moment and total spin angular momentum six–vectors are or are not constants of the motion. The Bhabha–Corben theory fits into the former scheme. The classical schemes are put into canonical form by using for each particle the relativistic connection between the momenta and the rest-mass, modified to include the effect of the kinetic and potential energies due to spin and dipole moment, as the Hamilton–Jacobi equation and the usual Poisson brackets for the translational and total spin variables. The Wentzel field and the λ-limiting process are used mainly in dealing with the field. The variational principle for the Bhabha–Corben equations is given with the field treated according to the limiting process of Dirac or the relativistic cutoff method of Feynman. The quantization is completed by using the analogy rules. The changes required when the interacting field is a vector meson field are discussed.