Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-07-03
Class.Quant.Grav. 19 (2002) 767-782
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 2 figures, one figure and references added, substantial extension of the discussion. To appear in Classical and Quan
Scientific paper
10.1088/0264-9381/19/4/309
The character of quantum corrections to the gravitational action of a conformally invariant field theory for a self-interacting scalar field on a manifold with boundary is considered at third loop-order in the perturbative expansion of the zero-point function. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. The associated spherical formulation for diagramatic evaluations reveals a non-trivial effect which the topology of the manifold has on the vacuum processes and which ultimately dissociates the dynamical behaviour of the quantised field from its behaviour in the absence of a boundary. The first surface divergence is evaluated and the necessity for simultaneous renormalisation of volume and surface divergences is shown.
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