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

Viorel Iftimie | Zendy; Radu Purice | Zendy

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

Author(s) -

Viorel Iftimie,

Radu Purice

Publication year - 2015

Publication title -

journal of spectral theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.063

H-Index - 19

eISSN - 1664-0403

pISSN - 1664-039X

DOI - 10.4171/jst/104

Subject(s) - covariant transformation , hamiltonian (control theory) , physics , mathematical physics , spectrum (functional analysis) , hamiltonian lattice gauge theory , gauge (firearms) , gauge covariant derivative , quantum electrodynamics , gauge theory , theoretical physics , quantum mechanics , mathematics , gauge anomaly , materials science , mathematical optimization , metallurgy

Using the procedures in \cite{Bu} and \cite{GMS} and the magnetic pseudodifferential calculus we have developped in \cite{MP1,MPR1,IMP1,IMP2} we construct an effective Hamitonian 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.

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