The Newtonian potential of a static Dirac spinor particle

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.

SOME REMARKS ON THE GRAVITATIONAL AHARONOV–BOHM EFFECT

A massless spinor particle is considered in the background spacetimes generated by a moving mass current and by a spinning cosmic string. In the weak field approximation it is shown that the solution of the Weyl equations depends on the velocity of the source, which does not affect the curvature in this approximation in the case of a moving mass current. In the case of a spinning cosmic string, the solution of the Weyl equations depends on the deficit angle and on the angular momentum of the string. These effects may be viewed as examples of the gravitational analogues of the Aharonov–Bohm effect in electrodynamics.

CANCELLATION OF ULTRAVIOLET DIVERGENCES FOR LOCALLY FLAT METRICS

We extend the work done for cosmic strings on the perturbative calculation of vacuum polarization of a massless field in the space–time of multiple cosmic strings and show that for a more general class of locally flat metrics, the one-loop calculation does not introduce any new divergences to the vev of the energy of a scalar particle or a spinor particle.

OPERATOR REGULARIZATION AND THE DIVERGENCE OF THE SUPERCURRENT

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the ζ-function. A perturbative expansion due to Schwinger allows one to compute from the ζ-function one-loop one-particle irreducible Green's functions. By regulating in this way, we do not have to compute Feynman diagrams, we avoid having to introduce a regulating parameter into the initial Lagrangian and we do not encounter any divergent integrals. This procedure is illustrated for N = 1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the super-current is recovered.