Ecuaciones de Hamilton-Jacobi y de Schrödinger en la dinámica relativista de tiempo propio

Abstract

The dynamics of a relativistic point particle is formulated using the proper time as evolution parameter on the hyperbolic $p_0^2-{\vec p}^2=M^2c^2$ and spheric $p_4^2+{\vec p}^2=\ce_0^2/c^2$ shells. This last case corresponds to considering the motion under a Lorentz invariant potential. The Hamilton-Jacobi equations of motion under this Lorentz scalar potential are formulated both for massive ($M^2=m^2,~m>0$) and massless ($M=0,~m>~0$) particles, and for the neutrino. We present additionally a first quatization version of the model following the Schrödinger canonical quatization scheme.