29 research outputs found
Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light
We present a Green's dyadic formulation to calculate the Casimir energy for a
dielectric-diamagnetic cylinder with the speed of light differing on the inside
and outside. Although the result is in general divergent, special cases are
meaningful. It is pointed out how the self-stress on a purely dielectric
cylinder vanishes through second order in the deviation of the permittivity
from its vacuum value, in agreement with the result calculated from the sum of
van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0
Searching for a C-function on the three-dimensional sphere
We present a detailed analytic study on the three-dimensional sphere of the most popular candidates for C-functions, both for Dirac and scalar free massive fields. We discuss to which extent the effective action, the RĂ©nyi entanglement entropy and the renormalized entanglement entropy fulfill the conditions expected from C-functions. In view of the absence of a good candidate in the case of the scalar field, we introduce a new candidate, which we call the modified effective action, and analyze its pros and cons.Instituto de FĂsica La Plat
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit ß/a « 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than 2p/ß , this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top UV¿>¿S top IR . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces
Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates
We calculate the lateral Casimir force between corrugated parallel plates,
described by -function potentials, interacting through a scalar field,
using the multiple scattering formalism. The contributions to the Casimir
energy due to uncorrugated parallel plates is treated as a background from the
outset. We derive the leading- and next-to-leading-order contribution to the
lateral Casimir force for the case when the corrugation amplitudes are small in
comparison to corrugation wavelengths. We present explicit results in terms of
finite integrals for the case of the Dirichlet limit, and exact results for the
weak-coupling limit, for the leading- and next-to-leading-orders. The
correction due to the next-to-leading contribution is significant. In the weak
coupling limit we calculate the lateral Casimir force exactly in terms of a
single integral which we evaluate numerically. Exact results for the case of
the weak limit allows us to estimate the error in the perturbative results. We
show that the error in the lateral Casimir force, in the weak coupling limit,
when the next-to-leading order contribution is included is remarkably low when
the corrugation amplitudes are small in comparison to corrugation wavelengths.
We expect similar conclusions to hold for the Dirichlet case. The analogous
calculation for the electromagnetic case should reduce the theoretical error
sufficiently for comparison with the experiments.Comment: 25 pages, 10 figures, appendix added, references corrected, typos
correcte
Surface Divergences and Boundary Energies in the Casimir Effect
Although Casimir, or quantum vacuum, forces between distinct bodies, or
self-stresses of individual bodies, have been calculated by a variety of
different methods since 1948, they have always been plagued by divergences.
Some of these divergences are associated with the volume, and so may be more or
less unambiguously removed, while other divergences are associated with the
surface. The interpretation of these has been quite controversial. Particularly
mysterious is the contradiction between finite total self-energies and surface
divergences in the local energy density. In this paper we clarify the role of
surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0
Non-contact gears: II. Casimir torque between concentric corrugated cylinders for the scalar case
The Casimir interaction between two concentric corrugated cylinders provides
the mechanism for non-contact gears. To this end, we calculate the Casimir
torque between two such cylinders, described by -potentials, which
interact through a scalar field. We derive analytic expressions for the Casimir
torque for the case when the corrugation amplitudes are small in comparison to
the corrugation wavelengths. We derive explicit results for the Dirichlet case,
and exact results for the weak coupling limit, in the leading order. The
results for the corrugated cylinders approach the corresponding expressions for
the case of corrugated parallel plates in the limit of large radii of cylinders
(relative to the difference in their radii) while keeping the corrugation
wavelength fixed.Comment: 9 pages, 3 figures, references correcte
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
Abstract: We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit β/a ≪ 1 of a massive field theory in 3-dimensional spherical spaces, M3, with constant curvature 6/a2. For masses lower than 2Ď€/β, this term can be identified with the free energy of the same theory on M3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, Shol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy Shol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. SUVtop > SIRtop. From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F -theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological RĂ©nyi entanglement entropy on disks of 2-dimensional flat spaces.Facultad de Ciencias ExactasInstituto de FĂsica La Plat
Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
We consider the electric and magnetic energy densities (or equivalently field
fluctuations) in the space around a point-like field source in its ground
state, after having subtracted the spatially uniform zero-point energy terms,
and discuss the problem of their singular behavior at the source's position. We
show that the assumption of a point-like source leads, for a simple Hamiltonian
model of the interaction of the source with the electromagnetic radiation
field, to a divergence of the renormalized electric and magnetic energy density
at the position of the source. We analyze in detail the mathematical structure
of such singularity in terms of a delta function and its derivatives. We also
show that an appropriate consideration of these singular terms solves an
apparent inconsistency between the total field energy and the space integral of
its density. Thus the finite field energy stored in these singular terms gives
an important contribution to the self-energy of the source. We then consider
the case of an extended source, smeared out over a finite volume and described
by an appropriate form factor. We show that in this case all divergences in
local quantities such as the electric and the magnetic energy density, as well
as any inconsistency between global and space-integrated local self-energies,
disappear.Comment: 8 pages. The final publication is available at link.springer.co
Evaluation of the Casimir Force for a Dielectric-diamagnetic Cylinder with Light Velocity Conservation Condition and the Analogue of Sellmeir's Dispersion Law
We study the Casimir pressure for a dielectric-diamagnetic cylinder subject
to light velocity conservation and with a dispersion law analogous to
Sellmeir's rule. Similarities to and differences from the spherical case are
pointed out.Comment: 19 pages Latex, no figures; discussion expanded. To appear in Physica
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