Spectrum of wormholes

Wormholes have been studied mainly in the semiclassical approximation as solutions of the classical Euclidean field equations. However, such solutions are rather special, and exist only for certain kinds of matter. On the other hand, one can represent wormholes in a more general manner as solutions of the Wheeler-DeWitt equation with appropriate boundary conditions. Minisuperspace models with massless minimal or conformal scalar fields have a discrete spectrum of these solutions. The Giddings-Strominger instanton solution corresponds to a sum of an infinite number of these solutions. Minisuperspace models with a massive scalar field also appear to have a discrete spectrum of such solutions, whose asymptotic form is given.