In I it has been shown that Schrödingers’s equation, which represents already an essential part of the quantum-theoretical formalism, can be derived from a number of statistical assumptions. In the present paper this theory has been generalized to gauge fields and spin. The treatment of gauge fields led to several remarkable new insights: We understand now why potentials (and not local fields) occur in the field equations of quantum theory. The non-uniqueness of the potentials and the related concept of gauge invariance becomes a comprehensible matter and is not a mystery any more. The functional form of the corresponding local force (Lorentz force) can also be derived. Both the results of I and of the present paper should, in our opinion, be interpreted as arguments in favor of the statistical interpretation of quantum theory. The remaining crucial question, in the non-relativistic domain of physics, is whether the present approach can be generalized to many particles. Assuming that this can be done, a further major problem for future research is a relativistic formulation of the present theory.