Abstract
Quantum gravitational bubbles may be used to obtain a non-perturbative approximation to the path integral of quantum gravity. There are three basic types of bubblesCP 2,S 2 ×S 2, andK3, and in this paper the propagation of elementary spin-1 particles inCP 2 is investigated. To date information about the propagation of particles other than scalars has been obtained by making approximations to the basic bubble types. The work presented here represents the first exact calculation. It is found that spin-1 particles scatter very strongly, particularly at low energies, which is at odds with both physical observation and the earlier work on this subject. Possible explanations for this discrepancy are offered.
Similar content being viewed by others
References
Hawking, S.W., Page, D.N., Pope, C.N.: The propagation of particles in spacetime foam. Phys. Lett. B86, 175 (1979)
Hawking, S.W., Page, D.N., Pope, C.N.: Quantum gravitational bubbles. Nucl. Phys. B170, 283 (1980)
Hawking, S.W.: The path integral approach to quantum gravity. In: Hawking, S.W., Israel, W. (eds.). General Relativity, Cambridge: Cambridge Univ. Press 1979
Freedman, M.H.: (in preparation)
Hitchin, N.: Compact four-dimensional Einstein manifolds. J. Diff. Geom.9, 435 (1975)
Gibbons, G.W., Pope, C.N.: The positive action conjecture and asymptotically Euclidean metrics in quantum gravity, Commun. Math. Phys.66, 267 (1979)
Page, D.N.: Phys. Lett. A physical picture of theK3 gravitational instanton80B, 55 (1978)
Warner, N.P.: Green's functions onCP n. Preprint, Cambridge
Gibbons, G.W., Pope, C.N.: ℂP 2 as a gravitational instanton. Commun. Math. Phys.61, 239 (1978)
Gibbons, G.W., Hawking, S.W.: Classification of gravitational instanton symmetries. Commun. Math. Phys.66, 291 (1979)
Gibbons, G.W., Pope, C.N.: ℂP 2 as a gravitational instanton. Commun. Math. Phys.61, 239 (1978)
Friedlander, F.G.: The wave equation on a curved space-time. Cambridge: Cambridge University Press 1975
Penrose, R.: Null hypersurface initial data for classical fields of arbitrary spin and for general relativity. Gen. Rel. Grav.12, 225 (1980)
Pope, C.N.: Eigenfunctions and spinc structures inCP 2. Preprint, Cambridge
Author information
Authors and Affiliations
Additional information
Communicated by S. Hawking
Rights and permissions
About this article
Cite this article
Warner, N.P. The scattering of spin-1 particles by quantum gravitational bubbles. Commun.Math. Phys. 86, 419–436 (1982). https://doi.org/10.1007/BF01212177
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01212177