  The Symmetries of Feynman Integrals method (SFI) associates a natural Lie
group with any diagram, depending only on its topology. The group acts on
parameter space and the method determines the integral's dependence within
group orbits. This paper analyzes the two-loop vacuum diagram. It is shown how
the solution of the SFI equations practically reproduces the most general value
of the integral. On the way certain novel derivations are found, a geometrical
interpretation is described, and divergences in general dimension are analyzed.
These would hopefully be useful for engaging with more involved diagrams.

High Energy Physics - Theory