Casimir forces between spheres and loop integrals

A summary of recent calculations of Casimir forces between a collection of $N$-dielectric spheres is presented. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. A loop integral formulation is also discussed where we rewrite the expressions for the force in terms of loop integrals for the effective classical propagation of the electric and magnetic fields.Comment: 5 pages, Contribution to Proceedings of QFEXT09, Norman O

On the etiology of trachoma

The importance of a study of this disease cannot be overestimated on account of the widespread suffer - in and inefficiency which have followed in its trail, from time immemorial. Within recent years it has been brought more to the notice of the British people y the Reports of the Royal Commission on Alien Immigration. Trachoma is imported into England, by and is found chiefly among aliens and their offspring. At the beginning of the last century it received great attention on account of its prevalence in those European armies that happened to be stationed in Egypt

Superimposed multi-resolution imaging

We present a novel approach to foveated imaging based on dual-aperture optics that superimpose two images on a single sensor, thus attaining a pronounced foveal function with reduced optical complexity. Each image captures the scene at a different magnification and therefore the system simultaneously captures a wide field of view and a high acuity at a central region. This approach enables arbitrary magnification ratios using a relatively simple system, which would be impossible using conventional optical design, and is of importance in applications where the cost per pixel is high. The acquired superimposed image can be processed to perform enhanced object tracking and recognition over a wider field of view and at an increased angular resolution for a given limited pixel count. Alternatively, image reconstruction can be used to separate the image components enabling the reconstruction of a foveated image for display. We demonstrate these concepts through ray-tracing simulation of practical optical systems with computational recovery

Casimir forces from a loop integral formulation

We reformulate the Casimir force in the presence of a non-trivial background. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials take place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued.Comment: references added, text clarified in place

Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions

We consider N=1 supersymmetric gauge theories in which the couplings are allowed to be space-time dependent functions. Both the gauge and the superpotential couplings become chiral superfields. As has recently been shown, a new topological anomaly appears in models with space-time dependent gauge coupling. Here we show how this anomaly may be used to derive the NSVZ beta function in a particular, well-determined renormalisation scheme, both without and with chiral matter. Moreover we extend the topological anomaly analysis to theories coupled to a classical curved superspace background, and use it to derive an all-order expression for the central charge c, the coefficient of the Weyl tensor squared contribution to the conformal anomaly. We also comment on the implications of our results for the central charge a expected to be of relevance for a four-dimensional C-theorem.Comment: 28 pages, LaTeX, no figure

Holography of a Composite Inflaton

We study the time evolution of a brane construction that is holographically dual to a strongly coupled gauge theory that dynamically breaks a global symmetry through the generation of an effective composite Higgs vev. The D3/D7 system with a background magnetic field or non-trivial gauge coupling (dilaton) profile displays the symmetry breaking. We study motion of the D7 brane in the background of the D3 branes. For small field inflation in the field theory the effective Higgs vev rolls from zero to the true vacuum value. We study what phenomenological dilaton profile generates the slow rolling needed, hence learning how the strongly coupled gauge theory's coupling must run. We note that evolution of our configuration in the holographic direction, representing the phyiscs of the strong interactions, can provide additional slowing of the roll time. Inflation seems to be favoured if the coupling changes by only a small amount or very gently. We speculate on how such a scenario could be realized away from N=4 gauge theory, for example, in a walking gauge theory.Comment: 13 pages, 12 figures; v2: Added reference