Decomposition of time-ordered products and path-ordered exponentials

We present a decomposition formula for U-n, an integral of time-ordered products of operators, in terms of sums of products of the more primitive quantities C-m, which are the integrals of time-ordered commutators of the same operators. The resulting factorization enables a summation over n to be carried out to yield an explicit expression for the time-ordered exponential, an expression which turns out to be an exponential function of C-m. The Campbell-Baker-Hausdorff formula and the non-Abelian eikonal formula obtained previously are both special cases of this result. (C) 1998 American Institute of Physics. [S0022-2488(98)00610-0].