ar X iv : q ua nt - p h / 05 05 12 8 v 2 1 6 A ug 2 00 5 A constructive algorithm for the Cartan decomposition of SU ( 2 N )

We present an explicit numerical method to obtain the Cartan-KhanejaGlaser decomposition of a general element G ∈ SU(2 ) in terms of its ‘Cartan’ and ‘non-Cartan’ components. This effectively factors G in terms of group elements that belong in SU(2) with n < N , a procedure that an be iterated down to n = 2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.