Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity

We study the point spectrum of the linearization at a solitary wave solution ϕω(x)e−iωt to the nonlinear Dirac equation in Rn, for all n≥1, with the nonlinear term given by f(ψ⁎βψ)βψ (known as the Soler model). We focus on the spectral stability, that is, the absence of eigenvalues with positive real part, in the non-relativistic limit ω→m−0, in the case when f∈C1(R∖{0}), f(τ)=|τ|κ+O(|τ|K) for τ→0, with 0