On Holland’s Frame for Randers Space and Its Applications in Physics

From a rigorous Finsler geometric perspective, we re-examine Holland’s Randers space theory of motion of an electron in flat Minkowski spacetime permeated with an electromagnetic field. Holland’s theory was motivated 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 anholonomy. 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.