Physics
Scientific paper
Dec 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..36.3593j&link_type=abstract
Physical Review D (Particles and Fields), Volume 36, Issue 12, 15 December 1987, pp.3593-3603
Physics
30
Scientific paper
In a previous paper, a modified effective-action formalism was developed which produces equations satisfied by the expectation value of the field, rather than the usual in-out average. Here this formalism is applied to a quantized scalar field in a background which is a small perturbation from Minkowski spacetime. The one-loop effective field equation describes the back reaction of created particles on the gravitational field, and is calculated in this paper to linear order in the perturbation. In this way we rederive an equation first found by Horowitz using completely different methods. This equation possesses exponentially growing solutions, so we confirm Horowitz's conclusion that flat spacetime is unstable in this approximation to the theory. The new derivation shows that the field equation is just as useful as the one-loop approximation to the in-out equation, contrary to earlier arguments. However, the instability suggests that the one-loop approximation cannot be trusted for gravity. These results are compared with the corresponding situation in QED and QCD.
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