  A framework for UV completing particle theories is proposed, based on the
worldline formalism, which is equivalent to weighting all sums over histories
with a proper-time dependent measure that has a smallest proper-time. We deduce
a criterion to avoid ghosts, and find that the ghost-free theories have the
(string-theory inspired) infinite-derivative model of Siegel as a special case,
but represent a significant generalisation. Generically, the UV of such
theories is dominated by a saddle-point in the proper-time, leading to
simplification in the computation of amplitudes. We focus on a particularly
attractive option which is to mimic the regulating properties of modular
invariance with a worldline "inversion symmetry".
