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} $\beta$-function.

Proceedings of International Tribology Conference (Hiroshima 2011.10.30-11.03), 20 pages, 7 figures

References in corpus (2)

• Casimir Energy of 5D Warped System and Sphere Lattice Regularization
• Geometric Approach to Quantum Statistical Mechanics and Minimal Area Principle

Cited by in corpus (2)

• Non-equilibrium Statistical Approach to Friction Models
• Renormalization Group Approach to Dissipative System