UV completion on the worldline

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 propertime dependent measure that has a smallest proper-time. We deduce a criterion to avoid ghosts, and nd that the ghost-free theories have the (string-theory inspired) innitederivative model of Siegel as a special case, but represent a signicant generalisation. Generically, the UV of such theories is dominated by a saddle-point in the proper-time, leading to simplication 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".