Spectral theory near thresholds for weak interactions with massive particles

Abstract : We consider a Hamiltonian describing the weak decay of the massive vector boson Z0 into electrons and positrons. We show that the spectrum of the Hamiltonian is composed of a unique isolated ground state and a semi-axis of essential spectrum. Using a suitable extension of Mourre's theory, we prove that the essential spectrum below the boson mass is purely absolutely continuous.
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Jean-Marie Barbaroux, Jérémy Faupin, Jean-Claude Guillot. Spectral theory near thresholds for weak interactions with massive particles. Journal of Spectral Theory, European Mathematical Society, 2016, 6 (3), pp.505-555. ⟨10.4171/JST/131⟩. ⟨hal-00957524⟩

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