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

Immigració a Ponent. Resultats d'una evolució

El treball analitza l’evolució de la darrera onada migratòria, la seva composició i la seva distribució en el territori i entre els nuclis municipals. Agafar l’àmbit de Ponent permet escapar a una escala comarcal i comparar una realitat més diversa que ofereix una perspectiva més àmplia. L’assentament de població nouvinguda i l’alteració d’alguns paràmetres demogràfics han transformat algunes localitats de Ponent i mostren una tendència cap al procés d’urbanització d’unes comarques tradicionalment rurals. L’anàlisi es realitza, principalment, a partir de les dades obtingudes de l’INE i de l’IDESCAT i d’entrevistes realitzades a persones amb responsabilitats tècniques i polítiques de les administracion

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

Casimir self-energy of a \delta-\delta' sphere

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions

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 Rényi 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 Física 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: 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 $\delta$-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