Resumo

YAMALEEV, R.M.; FERNANDEZ OSORIO, A.L.  e  RODRIGUEZ DGZ, A. R.. Ecuaciones de Hamilton-Jacobi y de Schrödinger en la dinámica relativista de tiempo propio. Rev. mex. fis. [online]. 2004, vol.50, n.5, pp.443-452. ISSN 0035-001X.

The dynamics of a relativistic point particle is formulated using the proper time as evolution parameter on the hyperbolic ρ₀² -ρ^→2 = M²c² and spheric ρ4² + P^→2 = ε₀²/ c² 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 (M² = m², 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.

Palavras-chave : Extensions of the classical theories of the mechanics; Hamilton-Jacobi; Newton; to the relativistic and quantum frame; proper time; massive and massless particles; neutrino.

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