 In the mid-1950s, Schwartz’s theory of distributions was used by Wightman (1956) to develop an abstract formulation of QFT, which later came to be known known as axiomatic quantum field theory. Mature statements of this formulation are presented in Wightman and Gårding (1964) and in Streater and Wightman (1964). It was further refined in the late 1960s by Bogoliubov, who explicitly placed axiomatic QFT in the rigged Hilbert space framework (Bogoliubov et al. 1975, p. 256). It is by now standard within the axiomatic approach to put forth the following six postulates: spectral condition (there are no negative energies or imaginary masses), vacuum state (it exists and is unique), domain axiom for fields (quantum fields correspond to operator-valued distributions), transformation law (unitary representation in the field-operator (and state) space of the restricted inhomogeneous Lorentz group – “restricted” means inversions are excluded, and “inhomogeneous” means that translations are included), local commutativity (field measurements at spacelike separated regions do not disturb one another), asymptotic completeness (the scattering matrix is unitary – this assumption is sometimes weakened to cyclicity of the vacuum state with respect to the polynomial algebra of free fields). Rigged Hilbert space entered the axiomatic framework by way of the domain axiom, so this axiom will be discussed in more detail below.