We calculate the thermal conductivity of electrons and muons kappa_{e-mu}produced owing to electromagnetic interactions of charged particles in neutronstar cores and show that these interactions are dominated by the exchange oftransverse plasmons (via the Landau damping of these plasmons innonsuperconducting matter and via a specific plasma screening in the presenceof proton superconductivity). For normal protons, the Landau damping stronglyreduces kappa_{e-mu} and makes it temperature independent. Protonsuperconductivity suppresses the reduction and restores the Fermi-liquidbehavior kappa_{e-mu} ~ 1/T. Comparing with the thermal conductivity ofneutrons kappa_n, we obtain kappa_{e-mu}> kappa_n for T>2 GK in normal matterand for any T in superconducting matter with proton critical temperaturesT_c>3e9 K. The results are described by simple analytic formulae.
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