Nonlinear Spinor Field

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Abstract
A classical spinor field is defined by a variational principle on a Lagrangian with quadratic Dirac and quartic Fermi terms. Localized (particle-like) solutions are found within a class of comparison functions which make the angular momentum stationary for a given charge. It is found that the existence of eigen-solutions depends in a radical way on the parameters of the Lagrangian, but that the observable properties of those solutions which do exist depend little on these parameters.