Wormholes and Goldstone Bosons

The quantum theory of a complex scalar field coupled to gravity is considered. A formalism for the semiclassical approach in Euclidean time is developed and used to study wormhole physics. The conserved global charge plays an essential role. Wormhole physics turns on only after the symmetry is spontaneously broken. An effective self-interaction for Goldstone bosons due to wormholes is shown to be a cosine potential, whose vacuum energy will be reduced by the cosmic expansion. Some implications and questions are discussed.