 Wightman’s “field axiomatics”, already mentioned above, is–besides AQFT–one of the two most prominent proposals, for an axiomatisation of QFT. Both originated in the 1950s and influenced each other in their formation. In Wightman’s field axiomatics, the entities upon which the axioms are imposed are smeared field operators, in fact polynomial algebras \(P(\mathcal{O})\) thereof. The crucial axioms are covariance, microcausality (spacelike separated field operators required to either commute or anticommute), and spectrum condition (positive energy in all Lorentz frames, so that the vacuum is a stable ground state). One shortcoming of this approach is that field operators are gauge-dependent and thereby arguably not qualified as directly representing physical quantities. Moreover, the use of unbounded field operators makes Wightman’s approach mathematically cumbersome.