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
Lebesgue spaces are function spaces associated to measure spaces , where is a set, is a σ-algebra of subsets of , and is a countably additive measure on . Let be the space of those complex-valued measurable functions on for which the Lebesgue integral of the square of the absolute value of the function is finite, i.e., for a function in ,