On Holland’s frame for Randers space and its applications in Physics, preprint

Abstract. From a rigorous Finsler geometric perspective, we re-examine Hol-land’s Randers space theory of motion of an electron in flat Minkowski space-time permeated with an electromagnetic field. Holland’s theory was moti-vated by analogy with plastic deformation and dislocation in Bravais crystals, through work of D. Bohm on Quantum Mechanics. We develop the anholonomic geometry of a Randers space using Holland’s frame and determine two Finsler connections, one of them the crystallographic connection, the other just Cartan’s connection expressed in terms of anholon-omy. Corresponding to these, we give two fully covariant versions of Holland’s theory each of which covers the case of a curved Minkowski space-time. The crystallographic theory with extra matter is most promising. The well-known approach of D. Bohm (see [BH]) to quantum mechanics casts quantum theory into a classical form so that classical and quantum physics can be more easily compared. As a result, the so-called “quantum potential ” arises as