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In the perturbative approach to quantum field theory it is common to replacethe propagator $i (p^{2}-m_{0}^{2}+i\varepsilon )^{-1}$ for a scalar field by asimilar expression, namely $iZ (p^{2}-m^{2}+i\varepsilon )^{-1}$, where theshift of the mass from $m_{0}$ to $m$ reflects the mass renormalization and theconstant~$Z$ is the renormalized field strength (or wave-function). We arguethat, contrary to general belief, the non-perturbative value of~$Z$ is notnecessarily equal to zero in case the two-point function of an interactingquantum field theory is, as expected, more singular on the light-cone than thecorresponding free field two-point function. If, however, (massless) photons orcomposite (unstable) particles are present, the condition $Z=0$ follows fromtwo qualitatively different arguments, one being a theorem due to Buchholz, theother a criterion due to Weinberg. Hence, the condition $Z=0$ is, after all, auniversal feature of realistic models of elementary particle physics, whichinclude massless or unstable particles. The results hold within a naturalframework which, in the case of gauge theories, requires Hilbert spacepositivity, and therefore the use of non-manifestly covariant gauges.

On the value of the non-perturbative field renormalization constant Z in gauge theories