Physics
Scientific paper
Apr 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..39.2234m&link_type=abstract
Physical Review D (Particles and Fields), Volume 39, Issue 8, 15 April 1989, pp.2234-2244
Physics
8
Theory Of Quantized Fields, Lagrangian And Hamiltonian Approach
Scientific paper
We study the λφ4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x)=(λ<φ2>)1/2 and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation.
Mazzitelli Francisco D.
Paz Juan-Pablo
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