Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-04-04
Class.Quant.Grav. 20 (2003) 2793-2814
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, 1 figure. Minor elucidations in the Appendix regarding the cut-off $ N_0$ and in p.4 regarding the gravitational act
Scientific paper
10.1088/0264-9381/20/13/325
The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the theory to second order in the scalar self-coupling pursued herein involves explicit calculations of up to third loop-order and reveals that, in addition to the renormalisation of the scalar self-coupling and scalar field, the removal of all divergences necessitates the introduction of conformally non-invariant counterterms proportional to $ R\Phi^2$ and $ K\Phi^2$ in the bare scalar action as well as counterterms proportional to $ RK^2$, $ R^2$ and $ RK$ in the gravitational action. The substantial backreaction effects and their relevance to the renormalisation procedure are analysed.
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