HIGHER-ORDER POLARIZATION ON THE POINCARE GROUP AND THE POSITION-OPERATOR

The quantization of the free relativistic spinning particle is revised on the basis of a group approach to quantization. In momentum space, the wavefunctions provide the minimal canonical representation of mass m and spin j of the Poincare group P+up. The quantization in configuration space requires, as in many other physical systems, polarizations of higher-order type. This higher-order polarization technique turns out to be a natural framework for studying localizability and to provide a position operator.