1994/04/14 by E. Elizalde, Emilio Elizalde, Klaus Kirsten +2 · 43 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Perturbation theory (quantum mechanics) #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum field theory #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Regularization (linguistics) #Renormalization #Riemann zeta function #Scalar (mathematics) #Scalar curvature #Scalar field #Scalar field theory #Spacetime #Zeta function regularization #hep-th
paper · pdf · doi:10.1103/physrevd.50.5137
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 50(8), 5137-5147 (American Physical Society) · 23 pages, LaTex, UB-ECM-PF 94/1
arxiv created 1994/04/14 · openalex publication_date 1994/10/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A derivation of the one-loop effective Lagrangian in the self-interacting O(N) scalar theory, in slowly varying gravitational fields, is presented (using \ensuremathζ-function regularization and heat-kernel techniques). The result is given in terms of the expansion in powers of the curvature tensors (up to quadratic terms) and their derivatives, as well as in derivatives of the background scalar field (up to second derivatives). The renormalization group improved effective Lagrangian is studied, which gives the leading-log approach of the whole perturbation theory. An analysis of the effective equations (back-reaction problem) on the static hyperbolic spacetime openR2\ifmmode×\else\texttimes\fiH2/\ensuremathΓ is carried out for the simplest version of the theory: m2=0 and N=1. The possibility of the existence of the solution openR2\ifmmode×\else\texttimes\fiH2/\ensuremathΓ, induced by purely quantum effects, is discussed.