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

R.M. Yamaleev, A.L. Fernández Osorio, A.R. Rodríguez Dgz., .

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.

Keywords


Extensions of the classical theories of the mechanics; Hamilton-Jacobi; Newton; to the relativistic, quantum frame; proper time; massive, massless particles; neutrino

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Revista Mexicana de Física

ISSN: 2683-2224 (on line), 0035-001X (print)

Bimonthly publication of Sociedad Mexicana de Física, A.C.
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