Thomas rotation and polarized light: A non-abelian geometric phase in optics

Abstract

We describe a non-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincare sphere in terms of the Pancharatnam phase.