XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

oleg olkhov

Geometrization of classical wave fields

The hypothesis is suggested that the Dirac equation for free particle and the Maxwell equation for electromagnetic waves are relations describing propagation of the space topological defects. The hypothesis is based on a radically new interpretation for the wave function when this function is considered not as a description of some wave process into the space but as a vector realizing representation of the fundamental group of the closed space-time 4--manifold. Such approach gives an opportunity to explain the wave-particle duality of quantum particles and electromagnetic waves and appearance of probabilities in the quantum mechanics formalism. Within suggested approach the light velocity appears to be some topological invariant and this fact explain its independence on the source movement. It is shown that the Dirac equation for hydrogen atom can also be interpreted as relation describing microscopic deformation of the space. Preliminary results are placed at hep-th/0605060