Thomas Rotation and Polarised Light: A non-Abelian Geometric Phase in Optics

Abstract

We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarised 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 Poincaré sphere in terms of the Pancharatnam phase.

14 pages, Latex file, one figure, to appear in Pramana J. Phys