The Peierls–Onsager effective Hamiltonian in a complete gauge covariant setting: determining the spectrum

Abstract

Using the procedures in [4] and [8] and the magnetic pseudodierential calculus we have developped in [17, 19, 12, 13] we construct an effective Hamiltonian that describes the spectrum in any compact subset of the real axis for a large class of periodic pseudodifferential Hamiltonians in a bounded smooth magnetic field, in a completely gauge covariant setting, without any restrictions on the vector potential and without any adiabaticity hypothesis.