Quantization via Deformation of Prequantization

Christian Duval (1, 2) , Mark J. Gotay (3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 PIMS - Pacific Institute for the Mathematical Sciences

We introduce the notion of a ''Souriau bracket'' on a prequantum circle bundle $Y$ over a phase space $X$ and explain how a deformation of $Y$ in the direction of this bracket provides a genuine quantization of $X$.

Mots clés: Geometric Quantization; Deformation Quantization

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Christian Duval, Mark J. Gotay. Quantization via Deformation of Prequantization. Reports on Mathematical Physics, 2012, 70 (03), pp.361-374. ⟨10.1016/S0034-4877(12)60051-2⟩. ⟨hal-00613582v3⟩