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

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

1994-08-26

arxiv.org/abs/hep-th/9408145v2

J.Phys. A27 (1994) 6799-6806

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0305-4470/27/20/017

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. 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 $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.

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