Abstract
Methods of inversion of integro-differential operators of thin linear antennas and also related to the dispersion interaction of the Casimir-Lifshitz force between two thin linear objects described by the dielectric constant in the form of Drude-Lorentz are considered. A new rigorous model for calculating Casimir-Lifshitz forces for thin dielectric or conductive filaments based on the Lorentz force is proposed. To determine correlations, the formulas of G.T. Markov, the fluctuation-dissipation theorem and the principle of detailed equilibrium with a thermal field were used. Analytical estimates of the obtained spectral integrals are performed in the far zone.
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