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 $\sigma$ of this model has the form $\sigma =\sigma_E+\sigma_{0}$, $\sigma_E>\sigma_{0}$, where \sigma_E is the world function of the pseudo-Euclidean space, \sigma_0 is a constant responsible for quantum effects. It is proportional to Planck's constant \hbar .