Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian

Details Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian

2008-01-07

arxiv.org/abs/0801.0940v5

Eur.Phys.J.C64:495-527,2009

Physics

Mathematical Physics

Significant revision, typos corrected and references added

Scientific paper

10.1140/epjc/s10052-009-1155-3

A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This last result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields.

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