Universal model of a D=4 spinning particle.

Abstract

A universal model for a $D=4$ spinning particle is constructed with the configuration space chosen as ${\mathrm{R}}^{3,1}\ifmmode\times\else\texttimes\fi{}{S}^{2}$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible world-line first-order invariants of the Poincar\'e group. Each combination of the four constant parameters entering the Lagrangian gives the model, which describes the proper irreducible Poincar\'e dynamics both at the classical and quantum levels, and thereby the construction uniformly embodies the massive, massless, and continuous helicity cases depending upon the special choice of parameters. For the massive case, the connection with the Souriau approach to elementary systems is established. A constrained Hamiltonian formulation is built and Dirac canonical quantization is performed for the model in the covariant form. An explicit realization is given for the physical wave functions in terms of smooth tensor fields on ${\mathrm{R}}^{3,1}\ifmmode\times\else\texttimes\fi{}{S}^{2}$. A one-parametric family of consistent interactions with general electromagnetic and gravitational fields is introduced in the massive case. The spin tensor is shown to satisfy the Frenkel-Nyborg equation with an arbitrary fixed gyromagnetic ratio in the limit of weakly varying electromagnetic field.