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Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance
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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.
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Cited by 1 Pith paper
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Casimir Effect in Stochastic Semi-Classical Gravity
The paper rederives the known Fermi-coordinate gravitational correction to the Casimir force, F/A = -g E_C, but does not derive the claimed stochastic semi-classical gravity correction.
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