Lorentz Group derivable from Polarization Optics

Abstract

The Lorentz group is the fundamental language for space-time symmetries of relativistic particles. This group can these days be derived from the symmetries observed in other branches of physics. It is shown that this group can be derived from optical filters. The group O(2,1) is appropriate for attenuation filters, while the O(3) group describes phase-shift filters. The combined operation leads to a two-by-two representation of the six-parameter Lorentz group. It is shown also that the bilinear representation of this group is the natural language for the polarization optics.

5 pages, LaTeX file, no figures; presented at the 21st International Colloquium on Group Theoretical Methods in Physics (Goslar, Germany, July, 1996), to be published in the Proceedings. See also Phys. Lett. A, {\bf 219} 26-32 (1996)