 Does the field interpretation also suffer from problems concerning non-localizability? In the section “Deficiencies of the Conventional Formulation of QFT” we already saw that, strictly speaking, field operators cannot be defined at points but need to be smeared out in the (finite and arbitrarily small) vicinity of points, giving rise to smeared field operators \(\hat{\phi}(f)\), which represent the weighted average field value in the respective region. This procedure leads to operator-valued distributions instead of operator-valued fields. The lack of field operators at points appears to be analogous to the lack of position operators in QFT, which troubles the particle interpretation. However, for position operators there is no remedy analogous to that for field operators: while even unsharply localized particle positions do not exist in QFT (see Halvorson and Clifton 2002, theorem 2), the existence of smeared field operators demonstrates that there are at least point-like field operators. On this basis Lupher (2010) proposes a “modified field ontology”.