11 research outputs found
Conformal Anomaly for Free Scalar Propagation on Curved Bounded Manifolds
The trace anomaly for free propagation in the context of a conformally
invariant scalar field theory defined on a curved manifold of positive constant
curvature with boundary is evaluated through use of an asymptotic heat kernel
expansion. In addition to their direct physical significance the results are
also of relevance to the holographic principle and to Quantum Cosmology.Comment: 8 pages. To appear in General Relativity and Gravitatio
Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary
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 and in the
bare scalar action as well as counterterms proportional to , and
in the gravitational action. The substantial backreaction effects and
their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the
cut-off and in p.4 regarding the gravitational action. Certain
reference-related ommission corrected. To appear in Classical and Quantum
Gravit
Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary
The effect of quantum corrections to a conformally invariant field theory for
a self-interacting scalar field on a curved manifold with boundary is
considered. The analysis is most easily performed in a space of constant
curvature the boundary of which is characterised by constant extrinsic
curvature. An extension of the spherical formulation in the presence of a
boundary is attained through use of the method of images. Contrary to the
consolidated vanishing effect in maximally symmetric space-times the
contribution of the massless "tadpole" diagram no longer vanishes in
dimensional regularisation. As a result, conformal invariance is broken due to
boundary-related vacuum contributions. The evaluation of one-loop contributions
to the two-point function suggests an extension, in the presence of matter
couplings, of the simultaneous volume and boundary renormalisation in the
effective action.Comment: 14 pages, 1 figure. Additional references and minor elucidating
remarks added. To appear in Classical and Quantum Gravit
Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
The mathematical formalism necessary for the diagramatic evaluation of
quantum corrections to a conformally invariant field theory for a
self-interacting scalar field on a curved manifold with boundary is considered.
The evaluation of quantum corrections to the effective action past one-loop
necessitates diagramatic techniques. 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. In
such a context the stated evaluations can be accomplished through a consistent
interpretation of the Feynman rules within the spherical formulation of the
theory for which the method of images allows. To this effect, the mathematical
consequences of such an interpretation are analyzed and the spherical
formulation of the Feynman rules on the bounded manifold is, as a result,
developed.Comment: 12 pages, references added. To appear in Classical and Quantum
Gravit
Perturbative Evaluation of the Zero-Point function for Self-Interacting Scalar Field on a Manifold with Boundary
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.Comment: 19 pages, 2 figures, one figure and references added, substantial
extension of the discussion. To appear in Classical and Quantum Gravit
Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry
The vacuum activity generated by the curvature of the Schwarzschild
black-hole geometry close to the event horizon is studied for the case of a
massless, conformal scalar field. The associated approximation to the unknown,
exact propagator in the Hartle-Hawking vacuum state for small values of the
radial coordinate above results in an analytic expression which
manifestly features its dependence on the background space-time geometry. This
approximation to the Hartle-Hawking scalar propagator on the Schwarzschild
black-hole geometry is, for that matter, distinct from all other. It is shown
that the stated approximation is valid for physical distances which range from
the event horizon to values which are orders of magnitude above the scale
within which quantum and backreaction effects are comparatively pronounced. An
expression is obtained for the renormalised in the
Hartle-Hawking vacuum state which reproduces the established results on the
event horizon and in that segment of the exterior geometry within which the
approximation is valid. In contrast to previous results the stated expression
has the superior feature of being entirely analytic. The effect of the
manifold's causal structure to scalar propagation is also studied.Comment: 34 pages, 2 figures. Published on line on October 16, 2009 and due to
appear in print in Gen.Rel.Gra
Bulk versus brane running couplings
A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is
considered. It has been observed previously by Goldberger and Wise that in such
a self-interacting scalar theory on the bulk with a conical singularity there
is mixing of renormalization of 4d brane couplings with that of the bulk
couplings. We study the influence of the running bulk couplings on the running
of the 4d brane couplings. We find that bulk quantum effects may completely
alter the running of brane couplings. In particular, the structure of the
Landau pole may be drastically altered and non-asymptotically free running may
turn into asymptotically safe (or free) behavior.Comment: 11 pages, no figures, REVTeX