An Aad Model of Point Particle and the Pauli Equation

The classical relativistic linear AAD interaction, introduced by the author, leads in the case of weak coupling to a pointlike particle capable to be submitted to quantization via Feynman's path integrals along the line adequate to the requirements of the Pauli equation. In the discussed nonrelativistic case of the model the concept of spin is considered within early Feynman's ideas. It is known that Feynmanian quantization is suitable for systems having a classical analogue. If such an analogue does not exist, e.g. as is the case for particles with spin, one encounters difficulties. In this context we want in the present work to illustrate the following facts: 1) the problem of spin could be attempted by renovating Feynman's spin idea [1], according to which a unit vector represents the spin germ cell in the nonrelativistic case; 2) this picture on spin could have the cause in Wigner's suggestion of the classical free point particle with internal degrees of freedom [2]; 3) such a point of view may have its deeper origin in the weak coupling model of linear interaction [3],[4],[5], in which the internal variables, products of AAD theory, adopt the status of canonically conjugate variables; 4) the model of linear relativistic interaction, even if based on the AAD theory, is able to yield its quantum versions on the levels both of Dirac [5] and Pauli equations. The model of above type, verified in [5] with the assumptions 1)-3), suggests that the relativistic variant of Feynman quantum formalism, leads to the Feynman-Gell-Mann equation [6], equivalent to the Dirac equation. The concept of particle, used in [5] and established on the unit vector n, which is associated with the particle internal variables, is the key tool for the Feynman non-relativistic way of quantization proposed in the present article. The model permits to evaluate the changes of this vector, involved in the given amplitude, as those potentially realizable in the classical picture. As a consequence, the standard action of the particle in the electromagnetic field can be expressed in the form of a chain of δ functions. Using such the time evolution of n, we can determine the propagator K S for the Pauli equation. In this work it is also indicated that some reformulation of theory for particles with the spin 1/2 within the Feynman path integrals, combined with progressive tools of AAD theory, could shed a new light on the …