 Quantum field theory (see the entry on  quantum field theory)  deals with systems with infinitely many degrees of freedom. For such systems, the algebra of observables that results from imposing canonical commutation relations admits of multiple Hilbert-space representations that are not unitarily equivalent to each other. This differs from the case of standard quantum mechanics, which deals with systems with finitely many degrees of freedom. For such systems, the corresponding algebra of observables admits of unitarily equivalent Hilbert-space representations.