BAKER-CAMPBELL-HAUSDORFF RELATION FOR SPECIAL UNITARY GROUPS SU(N)

Multiplication of two elements of the special unitary group SU(N) dete rmines uniquely a third group element. A Baket-Campbell-Hausdorff rela tion is derived which expresses the group parameters of the product (w ritten as an exponential) in terms of the parameters of the exponentia l factors. This requires the eigenvalues of three (N x N) matrices. Co nsequently, the relation can be stated analytically up to N = 4, in pr inciple. Similarity transformations encoding the time evolution of qua ntum-mechanical observables, for example, can be obtained by the same means.