Properties of the wormhole calculus

We adapt the rules, used by Coleman in the context of Euclidean gravity to show that the cosmological constant vanishes, to the simpler case of a scalar field theory. We compute one- and two-point functions in a variety of examples and in various approximations. We discover cases where wormholes make first-order phase transitions disappear, but permit second-order transitions. We find a peculiar propagator for a scalar field coupled quadratically to wormholes in the Hartree-Fock approximation. We discuss various ways to deal with the divergences caused by arbitrarily large numbers of subuniverses.