George Tsoupros 2002 Class. Quantum Grav. 19 767 doi:10.1088/0264-9381/19/4/309
George Tsoupros
Show affiliationsThe 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 renormalization can be best accomplished on a Riemannian manifold of positive 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 quantized field from its behaviour in the absence of a boundary. The first surface divergence is evaluated and the necessity for simultaneous renormalization of volume and surface divergences is shown.
53C20 Global Riemannian geometry, including pinching (See also 31C12, 58B20)
Issue 4 (21 February 2002)
Received 10 July 2001, in final form 29 November 2001
Published 6 February 2002
George Tsoupros 2002 Class. Quantum Grav. 19 767
J E Decker 2003 Metrologia 40 135
H Danared et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1003
A Bahraminasab et al 2009 New J. Phys. 11 103051
Donald R Holt 2009 Metrologia 46 167
Clemens Elster et al 2003 Metrologia 40 189
G F R Ellis 2009 J. Phys.: Conf. Ser. 189 012011
D M Fradkin 1978 J. Phys. A: Math. Gen. 11 1069
S Machida 2003 J. Phys. G: Nucl. Part. Phys. 29 1713
John F Beacom 2007 J. Phys.: Conf. Ser. 60 183