Again on Lorentz Force and Minkowshi Geometry

Here the problem of associating a Lorentz transformation valued function or a Lorentz moving frame to a given massive particle's worldline, describing the evolution of its four-velocity, will be discussed. This is equivalent to the problem of finding a Lorentz Force field that, acting on the massive particle, would produce its given worldline. We emphasise the geometrical character of Lorentz Force, its naturalness in Special Relativity and in other space-time theories having the Minkowskian one as its typical tangent space.The problem can also be viewed as a gauge choice in a SO(3) principal fiber bundle over the particle's worldline. This is a modern view of the approach to the problem given by Walker 1932 and unifies all the possible Lorentz force laws describing the same curve, since the magnetic parts of the fields associated to such forces are the local expressions, under the gauge choice, of a unique global SO(3) connection while the electric part of these fields are local expressions of a section of anassociated bundle.These discussions, as they are presented here, have the didactic value of linking many disciplines as Special and General Relativity, Differential Geometry, Manifolds, Gauge Theories and Connections, in a precise but very comprehensible way. Therefore they could be a stimulating complement for a course in Special Relativity, followed by advanced undergraduate students.