1,806 research outputs found
Casimir effect in rugby-ball type flux compactifications
As a continuation of the work in \cite{mns}, we discuss the Casimir effect
for a massless bulk scalar field in a 4D toy model of a 6D warped flux
compactification model,to stabilize the volume modulus. The one-loop effective
potential for the volume modulus has a form similar to the Coleman-Weinberg
potential. The stability of the volume modulus against quantum corrections is
related to an appropriate heat kernel coefficient. However, to make any
physical predictions after volume stabilization, knowledge of the derivative of
the zeta function, (in a conformally related spacetime) is also
required. By adding up the exact mass spectrum using zeta function
regularization, we present a revised analysis of the effective potential.
Finally, we discuss some physical implications, especially concerning the
degree of the hierarchy between the fundamental energy scales on the branes.
For a larger degree of warping our new results are very similar to the previous
ones \cite{mns} and imply a larger hierarchy. In the non-warped (rugby-ball)
limit the ratio tends to converge to the same value, independently of the bulk
dilaton coupling.Comment: 13 pages, 6 figures, accepted for publication in PR
Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
Zeta regularization has proven to be a powerful and reliable tool for the
regularization of the vacuum energy density in ideal situations. With the
Hadamard complement, it has been shown to provide finite (and meaningful)
answers too in more involved cases, as when imposing physical boundary
conditions (BCs) in two-- and higher--dimensional surfaces (being able to
mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero
depths). What we have considered is the {\it additional} contribution to the cc
coming from the non-trivial topology of space or from specific boundary
conditions imposed on braneworld models (kind of cosmological Casimir effects).
Assuming someone will be able to prove (some day) that the ground value of the
cc is zero, as many had suspected until very recently, we will then be left
with this incremental value coming from the topology or BCs. We show that this
value can have the correct order of magnitude in a number of quite reasonable
models involving small and large compactified scales and/or brane BCs, and
supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop
Quantum Field Theory under the Influence of External Conditions, QFEXT'05,
Barcelona, September 5-9, 200
Casimir piston for massless scalar fields in three dimensions
We study the Casimir piston for massless scalar fields obeying Dirichlet
boundary conditions in a three dimensional cavity with sides of arbitrary
lengths and where is the plate separation. We obtain an exact
expression for the Casimir force on the piston valid for any values of the
three lengths. As in the electromagnetic case with perfect conductor
conditions, we find that the Casimir force is negative (attractive) regardless
of the values of , and . Though cases exist where the interior
contributes a positive (repulsive) Casimir force, the total Casimir force on
the piston is negative when the exterior contribution is included. We also
obtain an alternative expression for the Casimir force that is useful
computationally when the plate separation is large.Comment: 19 pages,3 figures; references updated and typos fixed to match
published versio
Zeta-Function Regularization is Uniquely Defined and Well
Hawking's zeta function regularization procedure is shown to be rigorously
and uniquely defined, thus putting and end to the spreading lore about
different difficulties associated with it. Basic misconceptions,
misunderstandings and errors which keep appearing in important scientific
journals when dealing with this beautiful regularization method ---and other
analytical procedures--- are clarified and corrected.Comment: 7 pages, LaTeX fil
On the issue of imposing boundary conditions on quantum fields
An interesting example of the deep interrelation between Physics and
Mathematics is obtained when trying to impose mathematical boundary conditions
on physical quantum fields. This procedure has recently been re-examined with
care. Comments on that and previous analysis are here provided, together with
considerations on the results of the purely mathematical zeta-function method,
in an attempt at clarifying the issue. Hadamard regularization is invoked in
order to fill the gap between the infinities appearing in the QFT renormalized
results and the finite values obtained in the literature with other procedures.Comment: 13 pages, no figure
Spherical systems in models of nonlocally corrected gravity
The properties of static, spherically symmetric configurations are considered
in the framework of two models of nonlocally corrected gravity, suggested in S.
Deser and R. Woodard., Phys. Rev. Lett. 663, 111301 (2007), and S. Capozziello
et al., Phys. Lett. B 671, 193 (2009). For the first case, where the Lagrangian
of nonlocal origin represents a scalar-tensor theory with two massless scalars,
an explicit condition is found under which both scalars are canonical
(non-phantom). If this condition does not hold, one of the fields exhibits a
phantom behavior. Scalar-vacuum configurations then behave in a manner known
for scalar-tensor theories. In the second case, the Lagrangian of nonlocal
origin exhibits a scalar field interacting with the Gauss-Bonnet (GB) invariant
and contains an arbitrary scalar field potential. It is found that the GB term,
in general, leads to violation of the well-known no-go theorems valid for
minimally coupled scalar fields in general relativity. It is shown, however,
that some configurations of interest are still forbidden, whatever be the
scalar field potential and the GB-scalar coupling function, namely,
"force-free" wormholes (such that g_{tt}= const) and black holes with
higher-order horizons.Comment: 11 pages, no figures. References and comments added, a final form to
appear in PR
Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of
gravity where an arbitrary function of the GB invariant, , is added to
the General Relativity action. We show that such theory is endowed with a quite
rich cosmological structure: it may naturally lead to an effective cosmological
constant, quintessence or phantom cosmic acceleration, with a possible
transition from deceleration to acceleration. It is demonstrated in the paper
that this theory is perfectly viable, since it is compliant with Solar System
constraints. Specific properties of gravity in a de Sitter universe,
such as dS and SdS solutions, their entropy and its explicit one-loop
quantization are studied. The issue of a possible solution of the hierarchy
problem in modified gravities is addressed too.Comment: LaTeX file 20 pages, new subsections are adde
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