Cyclicity of a vacuum, and uniqueness of a vacuum are sometimes considered separately. Also, there is the property of asymptotic completeness—that the Hilbert state space is spanned by the asymptotic spaces H i n and H o u t , appearing in the collision S matrix. The other important property of field theory is the mass gap which is not required by the axioms—that the energy-momentum spectrum has a gap between zero and some positive number.