2001/03/16 by Stefano De Leo
Physics and Astronomy · #hep-th
published as Found.Phys.Lett. 14 (2001) 37-50 · 9 pages, AMS-TeX
arxiv created 2001/03/16 · arxiv updated 2009/11/30
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.