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.
Sobolev space
The Sobolev space formula_96 is also denoted by formula_97 It is a Hilbert space, with an important subspace formula_98 defined to be the closure of the infinitely differentiable functions compactly supported in formula_1 in formula_97 The Sobolev norm defined above reduces here to