par Schmitt, Philipp;Schotz, Matthias 
Référence Reviews in mathematical physics, 2150035
Publication Publié, 2021
Référence Reviews in mathematical physics, 2150035
Publication Publié, 2021
Article révisé par les pairs
| Résumé : | We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from C1+n with the Wick star product in arbitrary signature. Two special cases of such manifolds are the complex projective space CPn and the complex hyperbolic disc n. We generalize several older results to this setting: The construction of formal star products and their explicit description by bidifferential operators, the existence of a convergent subalgebra of "polynomial"functions, and its completion to an algebra of certain analytic functions that allow an easy characterization via their holomorphic extensions. Moreover, we find an isomorphism between the non-formal deformation quantizations for different signatures, linking, e.g., the star products on CPn and n. More precisely, we describe an isomorphism between the (polynomial or analytic) function algebras that is compatible with Poisson brackets and the convergent star products. This isomorphism is essentially given by Wick rotation, i.e. holomorphic extension of analytic functions and restriction to a new domain. It is not compatible with the - -involution of pointwise complex conjugation. |
