  One-loop string scattering amplitudes computed using the standard D0-brane
conformal field theory (CFT) suffer from infrared divergences associated with
recoil. A systematic framework to take recoil into account is the worldline
formalism, where fixed boundary conditions are replaced by dynamical D0-brane
worldlines. We show that, in the worldline formalism, the divergences that
plague the CFT are automatically cancelled in a non-trivial way. The amplitudes
derived in the worldline formalism can be reproduced by deforming the CFT with
a specific "recoil operator", which is bilocal and different from the ones
previously suggested in the literature.
