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.
CCR and CAR algebras
Let formula_16 be a Hilbert space. In the theory of operator algebras the CAR algebra is the unique C*-completion of the complex unital *-algebra generated by elements formula_37 subject to the relations
for any formula_28, formula_43.
When formula_16 is separable the CAR algebra is an AF algebra and in the special case formula_16 is infinite dimensional it is often written as formula_46.