Abstract
The gravitational theory including spinor particle is formulated with the suggestion of tetrad fields [Formula: see text] by Utiyama, Kibble and Weinberg.[Formula: see text] We might take the metric [Formula: see text] as a constraint, that is used the method of Lagrange multiplier. In the weak-field approximation we calculate the metric of a static Dirac spinor particle proton and obtain that the metric is a diagonal [Formula: see text] which coincides with the anticipative result of Newtonian Gravitational potential.
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