834 research outputs found
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
Topology, Mass and Casimir energy
The vacuum expectation value of the stress energy tensor for a massive scalar
field with arbitrary coupling in flat spaces with non-trivial topology is
discussed. We calculate the Casimir energy in these spaces employing the
recently proposed {\it optical approach} based on closed classical paths. The
evaluation of the Casimir energy consists in an expansion in terms of the
lengths of these paths. We will show how different paths with corresponding
weight factors contribute in the calculation. The optical approach is also used
to find the mass and temperature dependence of the Casimir energy in a cavity
and it is shown that the massive fields cannot be neglected in high and low
temperature regimes. The same approach is applied to twisted as well as spinor
fields and the results are compared with those in the literature.Comment: 18 pages, 1 figure, RevTex format, Typos corrected and references
adde
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
Temperature effect in the Casimir attraction of a thin metal film
The Casimir effect for conductors at arbitrary temperatures is theoretically
studied. By using the analytical properties of the Green functions and applying
the Abel-Plan formula to Lifshitz's equation, the Casimir force is presented as
sum of a temperature dependent and vacuum contributions of the fluctuating
electromagnetic field. The general results are applied to the system consisting
of a bulk conductor and a thin metal film. It is shown that a characteristic
frequency of the thermal fluctuations in this system is proportional to the
square root of a thickness of the metal film. For the case of the sufficiently
high temperatures when the thermal fluctuations play the main role in the
Casimir interaction, this leads to the growth of the effective dielectric
permittivity of the film and to a disappearance of the dependence of Casimir's
force on the sample thickness.Comment: LaTeX 2.09, 8 pages, no figure
Dynamical Casimir Effect with Semi-Transparent Mirrors, and Cosmology
After reviewing some essential features of the Casimir effect and,
specifically, of its regularization by zeta function and Hadamard methods, we
consider the dynamical Casimir effect (or Fulling-Davis theory), where related
regularization problems appear, with a view to an experimental verification of
this theory. We finish with a discussion of the possible contribution of vacuum
fluctuations to dark energy, in a Casimir like fashion, that might involve the
dynamical version.Comment: 11 pages, Talk given in the Workshop ``Quantum Field Theory under the
Influence of External Conditions (QFEXT07)'', Leipzig (Germany), September 17
- 21, 200
Effective Finite Temperature Partition Function for Fields on Non-Commutative Flat Manifolds
The first quantum correction to the finite temperature partition function for
a self-interacting massless scalar field on a dimensional flat manifold
with non-commutative extra dimensions is evaluated by means of dimensional
regularization, suplemented with zeta-function techniques. It is found that the
zeta function associated with the effective one-loop operator may be nonregular
at the origin. The important issue of the determination of the regularized
vacuum energy, namely the first quantum correction to the energy in such case
is discussed.Comment: amslatex, 14 pages, to appear in Phys. Rev.
Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
Explicit formulas for the zeta functions corresponding to
bosonic () and to fermionic () quantum fields living on a
noncommutative, partially toroidal spacetime are derived. Formulas for the most
general case of the zeta function associated to a quadratic+linear+constant
form (in {\bf Z}) are obtained. They provide the analytical continuation of the
zeta functions in question to the whole complex plane, in terms of series
of Bessel functions (of fast, exponential convergence), thus being extended
Chowla-Selberg formulas. As well known, this is the most convenient expression
that can be found for the analytical continuation of a zeta function, in
particular, the residua of the poles and their finite parts are explicitly
given there. An important novelty is the fact that simple poles show up at
, as well as in other places (simple or double, depending on the number of
compactified, noncompactified, and noncommutative dimensions of the spacetime),
where they had never appeared before. This poses a challenge to the
zeta-function regularization procedure.Comment: 15 pages, no figures, LaTeX fil
Hamiltonian approach to the dynamical Casimir effect
A Hamiltonian approach is introduced in order to address some severe problems
associated with the physical description of the dynamical Casimir effect at all
times. For simplicity, the case of a neutral scalar field in a one-dimensional
cavity with partially transmitting mirrors (an essential proviso) is
considered, but the method can be extended to fields of any kind and higher
dimensions. The motional force calculated in our approach contains a reactive
term --proportional to the mirrors' acceleration-- which is fundamental in
order to obtain (quasi)particles with a positive energy all the time during the
movement of the mirrors --while always satisfying the energy conservation law.
Comparisons with other approaches and a careful analysis of the interrelations
among the different results previously obtained in the literature are carried
out.Comment: 4 pages, no figures; version published in Phys. Rev. Lett. 97 (2006)
13040
Fluctuations of quantum fields via zeta function regularization
Explicit expressions for the expectation values and the variances of some
observables, which are bilinear quantities in the quantum fields on a
D-dimensional manifold, are derived making use of zeta function regularization.
It is found that the variance, related to the second functional variation of
the effective action, requires a further regularization and that the relative
regularized variance turns out to be 2/N, where N is the number of the fields,
thus being independent on the dimension D. Some illustrating examples are
worked through.Comment: 15 pages, latex, typographical mistakes correcte
- …