General Decomposition Theory of Ordered Exponentials.

A general decomposition theory of ordered exponentials is presented by reducing the problem to the decomposition of ordinary exponential operators in terms of the super-operator 9 defined by F(t)exp(dt9)G(t) = F(t+ dt)G(t). It is proved that f t+dt T exp (s)ds = exp[dt((t) + 9)]. Here T denotes the time ordering.