Multidimensional theories and path integral for particles with spin 1/2

A dynamic principle for spinor particles, leading directly to the Dirac equation, is formulated. In this approach, the wave function dependence on an additional evolution parameter, which had to be postulated in former approaches, is obtained automatically. It is shown that the description of the particle transition from the point xµ(x6) to the point xµ(x6+2ɛ), taking into account all possible transitions through intermediate points xµ(x6+ɛ), is equivalent to squaring the Dirac equation, i.e., to a transition to the case of scalar particles for weak electromagnetic fields. The introduction of electromagnetic interaction in the framework of a unified five-dimensional theory of gravitation and electromagnetism is also considered.