Algebra and quantum geometry of multifrequency resonance

M. V. Karasev ; E. M. Novikova

Izvestiya. Mathematics , Tome 74 (2010) no. 6, pp. 1155-1204.

Résumé

The algebra of symmetries of a quantum resonance oscillator in the case of three or more frequencies is described using a finite (minimal) basis of generators and polynomial relations. For this algebra, we construct quantum leaves with a complex structure (an analogue of classical symplectic leaves) and a quantum Kähler 2-form, a reproducing measure, and also the corresponding irreducible representations and coherent states.

Détail

Keywords: frequency resonance, algebra of symmetries, non-linear commutation relations, quantum Kähler forms, coherent states.

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