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
One of the most familiar examples of a Hilbert space is the Euclidean space consisting of three-dimensional vectors, denoted by , and equipped with the dot product. The dot product takes two vectors and , and produces a real number . If and are represented in Cartesian coordinates, then the dot product is defined by