Casimir Energy for concentric δ\delta-δ′\delta' spheres

We study the vacuum interaction of a scalar field and two concentric spheres defined by a singular potential on their surfaces. The potential is a linear combination of the Dirac-$\delta$ and its derivative. The presence of the delta prime term in the potential causes that it behaves differently when it is seen from the inside or from the outside of the sphere. We study different cases for positive and negative values of the delta prime coupling, keeping positive the coupling of the delta. As a consequence, we find regions in the space of couplings, where the energy is positive, negative or zero. Moreover, the sign of the $\delta'$ couplings cause different behavior on the value of the Casimir energy for different values of the radii. This potential gives rise to general boundary conditions with limiting cases defining Dirichlet and Robin boundary conditions what allows us to simulate purely electric o purely magnetic spheres.Comment: 9 pages, 8 figures We are submitting this manuscript for publication in Physical Review

Leading- and next-to-leading-order lateral Casimir force on corrugated surfaces

We derive explicit analytic expressions for the lateral force for two different configurations with corrugations, parallel plates and concentric cylinders. By making use of the multiple scattering formalism, we calculate the force for a scalar field under the influence of a delta-function potential that has sinusoidal dependence in one direction simulating the corrugations. By making a perturbative expansion in the amplitude of the corrugation we find the leading order for the corrugated concentric cylinders and the next-to-leading order for the corrugated parallel plates.Comment: 6 pages. Seventh Alexander Friedmann International Seminar on Gravitation and Cosmolog

Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point-splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.Comment: 24 pages, 6 figure

Casimir interaction between plane and spherical metallic surfaces

We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the non trivial situation where the sphere radius $R$, the plane-sphere distance $L$ and the plasma wavelength $\lambda_\P$ have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of $L/R$. For metallic nanospheres where $R, L$ and $\lambda_\P$ have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation (PFA) and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments performed with spheres of large radius $R\gg L$.Comment: 4 pages, new presentation (highlighting the novelty of the results) and added references. To appear in Physical Review Letter

PT-Symmetric Quantum Electrodynamics

The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\phi$ has a cubic self-interaction of the form $i\phi^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.Comment: 9 pages, no figures, revtex

The Casimir energy and PT-symmetric theories: The dielectric cylinder and unitarity of PT-symmetric QED.

Abstract not available