Neutrino flavor conversion in a neutrino background: Single- versus multi-particle description

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Abstract
In the early Universe, or near a supernova core, neutrino flavor evolution may be affected by coherent neutrino-neutrino scattering. We develop a microscopic picture of this phenomenon. We show that coherent scattering does not lead to the formation of entangled states in the neutrino ensemble and therefore the evolution of the system can always be described by a set of one-particle equations. We also show that the previously accepted formalism overcounts the neutrino interaction energy; the correct one-particle evolution equations for both active-active and active-sterile oscillations contain additional terms. These additional terms modify the index of refraction of the neutrino medium, but have no effect on oscillation physics.