  Relations between integrals of time-ordered product of operators, and their
representation in terms of energy-ordered products are studied. Both can be
decomposed into irreducible factors and these relations are discussed as well.
The energy-ordered representation was invented to separate various infrared
contributions in gauge theories. It is shown that the irreducible time-ordered
expressions can be used to accomplish the same purpose. Besides, it has the
added advantage of being factorizable.
