On the inversion of the integro-differential operator of a thin linear nanoantenna and dispersion forces

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.