Persistence amplitudes from numerical quantum gravity

P. D'Eath, A. Sornborger

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude exp(-Iclassical/ℏ), (1) where Iclassical is the Euclidean action of the classical solution joining the initial and final data. In certain cases the tree amplitude is exact. We study Iclassical, and hence the quantum amplitude, in the case of a spherically symmetric Riemannian gravitational field coupled to a spherically symmetric scalar field. The classical scalar field obeys an elliptic equation, which we solve using relaxation techniques, in conjunction with the field equations giving the gravitational field. An example of the transition from linearity to nonlinearity is presented and power-law behaviour of the action is demonstrated.

Original languageEnglish
Pages (from-to)3435-3447
Number of pages13
JournalClassical and Quantum Gravity
Issue number11
StatePublished - Nov 1998
Externally publishedYes


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