  In the Symmetries of Feynman Integrals (SFI) approach, a diagram's parameter
space is foliated by orbits of a Lie group associated with the diagram. SFI is
related to the important methods of Integrations By Parts and of Differential
Equations. It is shown that sometimes there exist a locus in parameter space
where the set of SFI differential equations degenerates into an algebraic
equation, thereby enabling a solution in terms of integrals associated with
degenerations of the diagram. This is demonstrated by the two-loop vacuum
diagram, where the algebraic locus can be interpreted as a threshold phenomenon
and is given by the zeros of the Baikov polynomial. In addition, the symmetry
group is interpreted geometrically as linear transformations of loop currents
which preserve the subspace of squared currents within the space of quadratics
in loop currents.
