THE EXPONENTIAL MAP FOR THE CONFORMAL-GROUP O(2, 4)

We present a general method to obtain a closed finite formula for the exponential map from the Lie algebra to the Lie group for the defining representation of orthogonal groups. Our method is based on the Hamil ton-Cayley theorem and some special properties of the generators of th e orthogonal group and is also independent of the metric. We present a n explicit formula for the exponential of generators of the SO+(p, q) groups with p + q = 6, in particular, dealing with the conformal group SO+(2, 4) which is homomorphic to the SU(2, 2) group. This result is needed in the generalization of U(1)-gauge transformations to spin-gau ge transformations where the exponential plays an essential role. We a lso present some new expressions for the coefficients of the secular e quation of a matrix.