Understanding quantum interference in General Nonlocality

In this paper we attempt to give a new understanding of quantum double-slit interference of fermions in the framework of General Nonlocality (GN) [J. Math. Phys. 49, 033513 (2008)] by studying the self-(inter)action of matter wave. From the metric of the GN, we derive a special formalism to interpret the interference contrast when the self-action is perturbative. According to the formalism, the characteristic of interference pattern is in agreement with experiment qualitatively. As examples, we apply the formalism to the cases governed by Schr\"odinger current and Dirac current respectively, both of which are relevant to topology. The gap between these two cases corresponds to the fermion magnetic moment, which is possible to test in the near future. In addition, a general interference formalism for both perturbative and non-perturbative self-actions is presented. By analyzing the general formalism we predict that in the nonperturbative limit there is no interference at all. And by comparison with the special formalism of Schr\"odinger current, the coupling strength of self-action in the limit is found to be $\infty$. In the perturbative case, the interference from self-action turns out to be the same as that from standard approach of quantum theory. Then comparing the corresponding coefficients quantitatively we conclude that the coupling strength of self-action in this case falls in the interval $[0,1]$.