The Wigner angle as an anholonomy in rapidity space

Abstract

A product of two non-collinear boosts (i.e., pure Lorentz transformations) can be written as the product of a boost and a rotation, the angle of rotation being known as Wigner’s angle. This paper demonstrates how the Wigner angle and final boost parameters can be calculated simply in terms of the initial boost parameters using hyperbolic trigonometry. It also demonstrates that the Wigner angle is the (negative) area of a rapidity triangle composed of the two non-collinear boosts and their resultant.