  We model spacetime foam by a gas of virtual wormholes. For a free scalar
field we derive the effective Lagrangian which accounts for the interaction
with spacetime foam and contains two additional non-local terms. One term
describes the scattering of scalar particles on virtual wormholes and
explicitly reproduces the Pauli-Villars regularization procedure. The second
term describes the back reaction of particles on the number density of
wormholes and introduces a self-interaction between particles.
