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
where the dot indicates the dot product in the Euclidean space of partial derivatives of each order. Sobolev spaces can also be defined when is not an integer.