Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance

Details Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance

2012-03-13

arxiv.org/abs/1203.2708v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Proceedings of International Tribology Conference (Hiroshima 2011.10.30-11.03), 18 pages, 4 figures

Scientific paper

Electromagnetism in substance is characterized by permittivity (dielectric constant) and permeability (magnetic permeability). They describe the substance property {\it effectively}. We present a {\it geometric} approach to it. Some models are presented, where the two quantities are geometrically defined. Fluctuation due to the micro dynamics (such as dipole-dipole interaction) is taken into account by the (generalized) path-integral. Free energy formula(Lifshitz 1954), for the material composed of three regions with different permittivities, is explained. Casimir energy is obtained by a new regularization using the path-integral. Attractive force or repulsive one is determined by the sign of the {\it renormalization-group} $\beta$-function.

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