Magnetic moment of an electron near a surface with dispersion

Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to the Dirac equation for a charged particle in a weak magnetic field yield a general formula for the magnetic moment correction in terms of any choice of electromagnetic mode functions. For two particular models, a non-dispersive dielectric and an undamped plasma, it is shown that, by using contour integration techniques over a complex wave vector, this can be simplified to a formula featuring just integrals over TE and TM reflection coefficients of the surface. Analysing the magnetic moment correction for several models of surfaces, we obtain markedly different results from the previously considered simplistic 'perfect reflector' model, which is due to the inclusion of physically important features of the surface like evanescent field modes and dispersion in the material. Remarkably, for a general dispersive dielectric surface, the magnetic moment correction of an electron nearby has a peak whose position and height can be tuned by choice of material parameters

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

On the Calculation of Finite Plastic Strains in Shell Intersections with Finite Elements

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On worst-case investment with applications in finance and insurance mathematics

We review recent results on the new concept of worst-case portfolio optimization, i.e. we consider the determination of portfolio processes which yield the highest worst-case expected utility bound if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. They are by construction non-constant ones and thus differ from the usual constant optimal portfolios in the classical examples of the Merton problem. A particular application of such strategies is to model crash possibilities where both the number and the height of the crash is uncertain but bounded. We further solve optimal investment problems in the presence of an additional risk process which is the typical situation of an insurer

Option pricing in affine generalized Merton models

In this article we consider affine generalizations of the Merton jump diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of European options. On the one hand, the Brownian motion part in the Merton model may be generalized to a log-Heston model, and on the other hand, the jump part may be generalized to an affine process with possibly state dependent jumps. While the characteristic function of the log-Heston component is known in closed form, the characteristic function of the second component may be unknown explicitly. For the latter component we propose an approximation procedure based on the method introduced in [Belomestny et al., J. Func. Anal., 2009]. We conclude with some numerical examples

Sonoluminescence as Quantum Vaccum Radiation

We argue that the available experimental data is not compatible with models of sonoluminescence which invoke dynamical properties of the interface without regard to the compositional properties of the trapped gas inside the bubble.Comment: 2 pages,Revtex,No figures,Submitted to PRL(comments

Connecting geodesics and security of configurations in compact locally symmetric spaces

A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure

Gauge Theories with Cayley-Klein SO(2;j)SO(2;j) and SO(3;j)SO(3;j) Gauge Groups

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure

Casimir-Polder interaction between an atom and a dielectric slab

We present an explicit analytic calculation of the energy-level shift of an atom in front of a non-dispersive and non-dissipative dielectric slab. We work with the fully quantized electromagnetic field, taking retardation into account. We give the shift as a two-dimensional integral and use asymptotic analysis to find expressions for it in various retarded and non-retarded limiting cases. The results can be used to estimate the energy shift of an atom close to layered microstructures.Comment: 10 pages, incl 7 figure

Stress Tensor Correlators in the Schwinger-Keldysh Formalism

We express stress tensor correlators using the Schwinger-Keldysh formalism. The absence of off-diagonal counterterms in this formalism ensures that the +- and -+ correlators are free of primitive divergences. We use dimensional regularization in position space to explicitly check this at one loop order for a massless scalar on a flat space background. We use the same procedure to show that the ++ correlator contains the divergences first computed by `t Hooft and Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio