Geodesic
Quantum Birkhoff normal forms
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 487-506

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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
Mots-clés : quantum analogue, algebra of observables, automorphism. 
@article{TMF_2009_160_3_a4,
     author = {A. Yu. Anikin},
     title = {Quantum {Birkhoff} normal forms},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {487--506},
     publisher = {mathdoc},
     volume = {160},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_3_a4/}
}
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A. Yu. Anikin. Quantum Birkhoff normal forms. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 487-506. http://geodesic.mathdoc.fr/item/TMF_2009_160_3_a4/