Regular Article - Theoretical Physics
Spinors in the Lorentz group and their implications for quantum mechanics
Laboratoire des Solides Irradiés, Ecole Polytechnique, CEA/DSM/IRAMIS, CNRS, Route de Saclay, 91128, Palaiseau Cedex, France
* e-mail: Gerrit.Coddens@polytechnique.fr
Published online: 18 March 2008
We investigate what the precise meaning is of a spinor in the rotation and Lorentz groups. We find that spinors correspond to a special coding of a group element. This is achieved by coding the whole reference frame into a special isotropic or “zero-length” vector. The precise form of that special vector in the Lorentz group is lacking in the literature, and this leads to some confusion, as the point that the coding can be complete has been missed. We then apply these ideas to quantum mechanics and find that the Dirac equation can be derived by just trying to describe a rotating electron.
© Springer-Verlag , 2008