A Method of E. Borel for Calculation of the Thomas Precession: The Geometric Phase in Relativistic Kinematic Velocity Space and Its Applications in Optics

摘要

In 1913, E. Borel (1871-1956) considered the relativistic kinematic rotation of a body that arises in the course of its orbital motion. In order to determine the angular velocity of this rotation, Borel introduced the notion of a kinematic space and applied the Gauss-Bonnet formula for a sphere of a unit radius. However, at that time, his results did not find practical applications and, soon, were forgotten. After the discovery of electron spin by S.A. Goudsmit and G.E. Uhlenbeck in 1925, real interest in this phenomenon was rekindled, and it was considered once again by L.H. Thomas in 1926-1927, being termed the Thomas precession. The Thomas precession manifests itself mostly in optical phenomena.