Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Hilbert metric
Let Ω be a convex open domain in a Euclidean space that does not contain a line. Given two distinct points "A" and "B" of Ω, let "X" and "Y" be the points at which the straight line "AB" intersects the boundary of Ω, where the order of the points is "X", "A", "B", "Y". Then the Hilbert distance "d"("A", "B") is the logarithm of the cross-ratio of this quadruple of points: