Spinor extended Lorentz-force like equations as consequence of a spinorial structure of space-time

摘要

As previously shown, the special relativistic dynamical equation of theLorentz force type can be regarded as a consequence of a succession ofspace-time dependent infinitesimal Lorentz boosts and rotations. This insightindicate that the Lorentz-Force-like equation has a fundamental meaning inphysics. We show how this result may be spinorially obtained starting out outfrom the application of an infinitesimal element of SL(2,C) to the individualspinors, which are regarded here as being more fundamental objects thanfour-vectors. In this way we get a set of new dynamical spinor equationsinducing the extended Lorentz-Force-like equation in the Minkowski space-timeand geometrically obtain the spinor form of the electromagnetic field tensor.The term extended refers to the dynamics of some additional degrees of freedomthat may be associated with the intrinsic spin, namely, with the dynamics ofthree spacelike mutually orthogonal four-vectors, all of them orthogonal to thelinear four-momentum of the object under consideration that finally, in theparticle's proper frame. are identified with the generators of SU(2).