000057076 001__ 57076 000057076 005__ 20170504090233.0 000057076 0247_ $$2doi$$a10.1103/PhysRevD.94.065003 000057076 0248_ $$2sideral$$a96683 000057076 037__ $$aART-2016-96683 000057076 041__ $$aeng 000057076 100__ $$aShajesh, K.V. 000057076 245__ $$aCasimir energies of self-similar plate configurations 000057076 260__ $$c2016 000057076 5060_ $$aAccess copy available to the general public$$fUnrestricted 000057076 5203_ $$aWe construct various self-similar configurations using parallel d-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to the electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning d-function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases, the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green''s function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory. 000057076 536__ $$9info:eu-repo/grantAgreement/ES/DGA/2013-E242-2$$9info:eu-repo/grantAgreement/ES/UZ/CUD2015-12 000057076 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000057076 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000057076 700__ $$aBrevik, I. 000057076 700__ $$0(orcid)0000-0002-5575-6775$$aCavero-Peláez, I. 000057076 700__ $$aParashar, P. 000057076 773__ $$g94, 6 (2016), 065003 [13 pp]$$pPhys. rev., D Part. fields gravit. cosmol.$$tPHYSICAL REVIEW. D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY$$x1550-7998 000057076 8564_ $$s351884$$uhttps://zaguan.unizar.es/record/57076/files/texto_completo.pdf$$yVersión publicada 000057076 8564_ $$s118331$$uhttps://zaguan.unizar.es/record/57076/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000057076 909CO $$ooai:zaguan.unizar.es:57076$$particulos$$pdriver 000057076 951__ $$a2017-05-04-09:00:11 000057076 980__ $$aARTICLE