Gas of wormholes in Euclidean quantum field theory

We model the spacetime foam picture by a gas of wormholes in Euclidean field theory. A class of exact Green functions for a single wormhole is obtained in an explicit form. An iteration scheme which allows us to construct the exact Green function for a gas of wormholes is suggested. It is also shown that at large distances the presence of such a gas merely leads to a renormalization of mass and charge values. We also demonstrate that there exists a class of specific distributions of pointlike wormholes which essentially change the ultraviolet behavior of Green functions and lead to finite quantum field theories.