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Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary

George Tsoupros
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Abstract

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 $ RΦ^2$ and $ KΦ^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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George Tsoupros. 2003-04-27. Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary. https://doi.org/10.1088/0264-9381%2F20%2F13%2F325

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