The exponential map for the unitary group SU(2,2)

A. O. Barut; J. R. Zeni; A. J. Laufer

doi:10.1088/0305-4470/27/20/017

paper

The exponential map for the unitary group SU(2,2)

arXiv:hep-th/9408145 · doi:10.1088/0305-4470/27/20/017

Abstract

In this article we extend our previous results for the orthogonal group, $S O (2, 4)$ , to its homomorphic group $S U (2, 2)$ . Here we present a closed, finite formula for the exponential of a $4 \times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $S L (4, C)$ group. We apply this result to the $S U (2, 2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $S U (2, 2)$ can be written by means of the Dirac matrices.

10 pages