Spectra of relativistic Schrödinger operators with magnetic vector potentials (Q1327628)

The Hamiltonian of a relativistic particle of mass \(m\) with magnetic vector potential \(a(x)\) and an electric potential \(V(x)\) has the form (1) \(H = h^ w(x,D) + V(x)\), where \[ h^ w (x,D)u(x) = \iint e^{i(x-y) \xi} h \left( {x + y \over 2}, \xi \right) u(y) (2\pi)^{-n} dy d \xi; \quad x, \xi \in R^ n,\;m > 0, \] \(h(x,\xi) = \sqrt {| \xi - a(x)|^ 2 + m^ 2}\). The essential spectrum of the operator (1) is investigated.