  Integration By Parts (IBP) is an important method for computing Feynman
integrals. This work describes a formulation of the theory involving a set of
differential equations in parameter space, and especially the definition and
study of an associated Lie group G. The group acts on parameter space and
foliates it into G-orbits. The differential equations essentially provide the
gradient of the integral within the orbit in terms of integrals associated with
degenerate diagrams. In this way the computation of a Feynman integral at a
general point in parameter space is reduced to the evaluation of the Feynman
integral at some freely chosen base point on the same orbit, together with a
line integral inside the G-orbit and the degenerate integrals along the path.
This paper restricts to vacuum diagrams and integrals without numerators, but
the method is expected to generalize. The method is demonstrated by application
to the two-loop vacuum diagram. A relation between the reducibility of a
diagram though IBP and the reducibility of the associated electric circuit
though the Y-Delta transform is speculated.
