This article is cited in 5 papers

Quantum Birkhoff normal forms

A. Yu. Anikin

N. E. Bauman Moscow State Technical University, Moscow, Russia

Abstract: We consider quantum analogues of several theorems on Birkhoff normal forms and prove a quantum analogue of the theorem on reducing a Hamiltonian to the normal form and the analogue of the theorem on reducing a Hamiltonian to the real normal form. We obtain the normal form explicitly in the nonresonant case. We consider the uniqueness problems of the normal form and of the normalizing transformation in the nonresonant and resonant cases.

Keywords: Birkhoff normal form, quantum analogue, algebra of observables, automorphism.

Received: 15.10.2008

DOI: 10.4213/tmf6411

 English version: Theoretical and Mathematical Physics, 2009, 160:3, 1274–1291

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