On the Magic Matrix by Makhlin and the B-C-H Formula in SO(4)

Abstract

A closed expression to the Baker-Campbell-Hausdorff (B-C-H) formula in SO(4) is given by making use of the magic matrix by Makhlin. As far as we know this is the {\bf first nontrivial example} on (semi-) simple Lie groups summing up all terms in the B-C-H expansion.Comment: Latex ; 11 pages ; 1 figure ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.5 or 6), 200