Non-Riemannian model of the space-time responsible for quantum effects

A class of homogeneous isotropic space-time models including pseudo-Euclidean space as a special case is considered. Such a model is chosen, where the particle motion is described in the most adequate way. It means that the world tubes of all free particles (both classical and quantal) are characteristic geometrical structures of the space-time. The world function $σ $ of this model has the form $σ =σ_E+σ_0$, $σ_E>σ_0$, where σ_E is the world function of the pseudo-Euclidean space, σ_0 is a constant responsible for quantum effects. It is proportional to Planck's constant \hbar .