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Zero-point fluctuations in the background of a cosmic string provide an opportunity to study the effects of topology in quantum field theory. We use a scattering theory approach to compute quantum corrections to the energy density of a cosmic string, using the “ballpoint pen” and “flowerpot” models to allow for a nonzero string radius. For computational efficiency, we consider a massless field in 2+1 dimensions. We show how to implement precise and unambiguous renormalization conditions in the presence of a deficit angle, and make use of Kontorovich-Lebedev techniques to rewrite the sum over angular momentum channels as an integral on the imaginary axis.more » « less
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Klimchitskaya, Galina L.; Mostepanenko, Vladimir M. (Ed.)Using the formulation of the electromagnetic Green’s function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir–Polder interaction energy of a cone with a polarizable particle. We introduce this formalism by first reviewing the analogous approach for a perfectly conducting wedge, and then demonstrate the calculation through numerical evaluation of the resulting integrals.more » « less
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The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects’ electromagnetic response, the necessary calculations in quantum field theory are most naturally expressed in terms of electromagnetic scattering from each object. In this review, we illustrate a variety of such techniques, with a focus on those that can be expressed in terms of surface effects, including both idealized boundary conditions and their physical realization in terms of material properties. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 72 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.more » « less
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