529 research outputs found
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
Hawking Radiation for Non-minimally Coupled Matter from Generalized 2D Black Hole Models
It is well known that spherically symmetric reduction of General Relativity
(SSG) leads to non-minimally coupled scalar matter. We generalize (and correct)
recent results to Hawking radiation for a class of dilaton models which share
with the Schwarzschild black hole non-minimal coupling of scalar fields and the
basic global structure. An inherent ambiguity of such models (if they differ
from SSG) is discussed. However, for SSG we obtain the rather disquieting
result of a negative Hawking flux at infinity, if the usual recipe for such
calculations is applied.Comment: 8 page
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
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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
Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory
We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2
and
Vacuum energy in the presence of a magnetic string with delta function profile
We present a calculation of the ground state energy of massive spinor fields
and massive scalar fields in the background of an inhomogeneous magnetic string
with potential given by a delta function. The zeta functional regularization is
used and the lowest heat kernel coefficients are calculated. The rest of the
analytical calculation adopts the Jost function formalism. In the numerical
part of the work the renormalized vacuum energy as a function of the radius
of the string is calculated and plotted for various values of the strength of
the potential. The sign of the energy is found to change with the radius. For
both scalar and spinor fields the renormalized energy shows no logarithmic
behaviour in the limit , as was expected from the vanishing of the heat
kernel coefficient , which is not zero for other types of profiles.Comment: 30 pages, 10 figure
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics
Divergencies in the Casimir energy for a medium with realistic ultraviolet behavior
We consider a dielectric medium with an ultraviolet behavior as it follows
from the Drude model. Compared with dilute models, this has the advantage that,
for large frequencies, two different media behave the same way. As a result one
expects the Casimir energy to contain less divergencies than for the dilute
media approximation. We show that the Casimir energy of a spherical dielectric
ball contains just one divergent term, a volume one, which can be renormalized
by introducing a contact term analogous to the volume energy counterterm needed
in bag models.
PACS: 12.20.Ds, 03.70.+k, 77.22.ChComment: article style, 10 page
Kaluza-Klein Pistons with non-Commutative Extra Dimensions
We calculate the scalar Casimir energy and Casimir force for a
Kaluza-Klein piston setup in which the extra dimensional space contains a
non-commutative 2-sphere, . The cases to be studied are and respectively as extra dimensional spaces, with the
dimensional commutative torus. The validity of the results and the
regularization that the piston setup offers are examined in both cases. Finally
we examine the 1-loop corrected Casimir energy for one piston chamber, due to
the self interacting scalar field in the non-commutative geometry. The
computation is done within some approximations. We compare this case for the
same calculation done in Minkowski spacetime . A discussion on the
stabilization of the extra dimensional space within the piston setup follows at
the end of the article.Comment: 22 page
Neutrino magnetic moment in a magnetized plasma
The contribution of a magnetized plasma to the neutrino magnetic moment is
calculated. It is shown that only part of the additional neutrino energy in
magnetized plasma connecting with its spin and magnetic field strength defines
the neutrino magnetic moment. It is found that the presence of magnetized
plasma does not lead to the considerable increase of the neutrino magnetic
moment in contrast to the results presented in literature previously.Comment: 7 page, 1 figures, based on the talk presented by E.N.Narynskaya at
the XVI International Seminar Quarks'2010, Kolomna, Moscow Region, June 6-12,
2010, to appear in the Proceeding
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