SPINNING PARTICLES ON SPACELIKE HYPERSURFACES AND THEIR REST FRAME DESCRIPTION

Abstract

A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. It is the pseudoclassical basis of the positive energy [Formula: see text] [or negative energy [Formula: see text]] part of the [Formula: see text] solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total four-momentum of the isolated system (when it is timelike). We find that on such hyperplanes these spinning particles have a nonminimal coupling only of the type "spin–magnetic field," like the nonrelativistic Pauli particles to which they tend in the nonrelativistic limit. The Lienard–Wiechert potentials associated with these charged spinning particles are found. Then, a comment is made on how to quantize the spinning particles respecting their fibered structure describing the spin structure.