Beyond the single universe

Abstract

Wormholes are going to play a rather crucial role in any theory of quantum gravity. In this paper a method is discussed for describing the statistics associated with a single wormhole in terms of probabilities and correlation functions, and their generating functionals, relative both to an observer living in Euclidean time and an observer in the asympotic region. We obtain matrix elements between vacuum states, filtered by the quantum state of the wormhole, of the same form as those which were recently discussed by Hawking and others for Abelian matter fields. For non-Abelian gauge fields, the matrix elements turn out to be given in terms of the field intensities rather than the fields themselves. In generalizing the procedure for obtaining wormhole-filtered generating functionals, we had to introduce the notion of cosmological spin which turned out to be responsible for providing the quantum state of a single universe with an observable character. It has been also seen that baby universes are in highly non-classical states describable as localized squeezed states of space-time.