5 Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. ε-away below the two-boson threshold) spectrum of Fröhlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension d ≥ 3. It contains a single polaron branch defined for total momentum p ∈ G (0) , where G (0) ⊂ ℝ d is a bounded domain, and, for any p ∈ ℝ d , a manifold of polaron + one-boson states with boson momentum q in a bounded domain depending on p. The polaron becomes unstable and dissolves into the one-boson manifold at the boundary of G (0) . The dispersion laws and generalized eigenfunctions are calculated.

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