Canonical formalism and quantization of world-line in a curved background metric

After discussing three various approaches to the canonical formalism for a world-line in a curved background metric it is developed a new covariant formalism. It is based on the Hamiltonian which, for tau = s, is equal to the proper mass and it generates translations in proper time s. The resulting Poisson-bracket relations are equivalent to the geodesic equation. In the quantized theory the classical 4-velocity usup(μ) is replaced by the operator γsup(μ) (Dirac matrices); the resulting Heisenberg equations are quantum analogue of the Papapetrou's equation for a spinning particle in a gravitational field. Our theory also predicts in a natural way the existence of an infinite bare mass term in the Lagrangian for the Dirac (or Klein-Gordon) equation and thus provides a deeper understanding of the ''renormalization'' procedure