Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance
Abstract
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} -function.
Keywords
Cite
@article{arxiv.1203.2708,
title = {Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance},
author = {Shoichi Ichinose},
journal= {arXiv preprint arXiv:1203.2708},
year = {2012}
}
Comments
Proceedings of International Tribology Conference (Hiroshima 2011.10.30-11.03), 20 pages, 7 figures