Path integrals and the indefiniteness of the gravitational action

by: GW Gibbons, SW Hawking, MJ Perry

Nuclear Physics B, Vol. 138, No. 1. (5 June 1978), pp. 141-150.

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Abstract

The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies.

@article{citeulike:1320400, abstract = {The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies.}, author = {Gibbons, G. W. and Hawking, S. W. and Perry, M. J. }, citeulike-article-id = {1320400}, journal = {Nuclear Physics B}, keywords = {cosmology}, month = {June}, number = {1}, pages = {141--150}, posted-at = {2007-05-23 06:49:56}, priority = {2}, title = {Path integrals and the indefiniteness of the gravitational action}, url = {http://www.sciencedirect.com/science/article/B6TVC-4718WD6-110/2/6b49cb72328fc44ea0a8a8e17f2795a3}, volume = {138}, year = {1978} }

RIS record

TY - JOUR ID - citeulike:1320400 L3 - citeulike-article-id:1320400 N2 - The Euclidean action for gravity is not positive definite unlike those of scalar and Yang-Mills fields. Indefiniteness arises because conformal transformations can make the action arbitrarily negative. In order to make the path integral converge one has to take the contour of integration for the conformal factor to be parallel to the imaginary axis. The path integral will then converge at least in the one-loop approximation if a certain positive action conjecture holds. We perform a zeta function regularization of the one-loop term for gravity and obtain a non-trivial scaling behaviour in cases in which the background metric has non-zero curvature tensor, and hence non-trivial topologies. IS - 1 JF - Nuclear Physics B EP - 150 TI - Path integrals and the indefiniteness of the gravitational action VL - 138 SP - 141 KW - cosmology AU - Gibbons, GW AU - Hawking, SW AU - Perry, MJ PY - 1978/06/05/ UR - http://www.sciencedirect.com/science/article/B6TVC-4718WD6-110/2/6b49cb72328fc44ea0a8a8e17f2795a3 ER -

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