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 space
This subsection employs the Hilbert projection theorem. If is a non-empty closed convex subset of a Hilbert space and a point in , there exists a unique point that minimizes the distance between and points in ,