 In contrast, Algebraic Quantum Field Theory (AQFT)—the most successful attempt to reformulate QFT axiomatically—employs only bounded operators. It builds upon work in the 1940s by Gelfand, Neumark, and in particular Segal, who tried to describe quantum physics in terms of \(C\)*-algebras [section 4.1. in the entry Quantum Theory and Mathematical Rigour has a more detailed account]. The notion of a \(C\)*-algebra generalizes the notion of the algebra \(\mathcal{B(H)}\) of all bounded operators on a Hilbert space \(\mathcal{H}\), which is also the most important example for a \(C\)*-algebra. In fact, it can be shown that any \(C\)*-algebra is isomorphic to a (norm-closed, self-adjoint) algebra of bounded operators on a Hilbert space. The boundedness (and self-adjointness) of the operators is the reason why \(C\)*-algebras are considered as ideal for representing physical observables. The ‘C’ indicates that one is dealing with a complex vector space and the ‘*’ refers to the operation that maps an element \(A\) of an algebra to its involution (or adjoint) \(A\)*, which generalizes the conjugate complex of complex numbers to operators. This involution is needed in order to define the crucial norm property of \(C\)*-algebras, which is of central importance for the proof of the above isomorphism claim.