The exponential of the spin representation of the Lorentz algebra

Jason Hanson

Published 2012-01-29Version 1

As discussed in a previous article, any (real) Lorentz algebra element possess a unique orthogonal decomposition as a sum of two mutually annihilating decomposable Lorentz algebra elements. In this article, this concept is extended to the spin representation of the Lorentz algebra. As an application, a formula for the exponential of the spin representation is obtained, as well as a formula for the spin representation of a proper orthochronous Lorentz transformation.