Universität zu Köln

Barmeier, Severin ORCID: 0000-0002-3779-2828 and Schmitt, Philipp (2023). Strict Quantization of Polynomial Poisson Structures. Commun. Math. Phys., 398 (3). S. 1085 - 1128. NEW YORK: SPRINGER. ISSN 1432-0916

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Abstract

We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on R-d, generalizing known results for constant and linear Poisson structures to polynomial Poisson structures of arbitrary degree. We give several examples of nonlinear Poisson structures and construct explicit formal star products whose deformation parameter can be evaluated to any real value of (h) over bar, giving strict quantizations on the space of analytic functions on R-d with infinite radius of convergence. We also address further questions such as continuity of the classical limit (h) over bar -> 0, compatibility with *-involutions, and the existence of positive linear functionals. The latter can be used to realize the strict quantizations as *-algebras of operators on a pre-Hilbert space which we demonstrate in a concrete example.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Barmeier, Severin UNSPECIFIED orcid.org/0000-0002-3779-2828 UNSPECIFIED Schmitt, Philipp UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-672778
DOI:	10.1007/s00220-022-04541-4
Journal or Publication Title:	Commun. Math. Phys.
Volume:	398
Number:	3
Page Range:	S. 1085 - 1128
Date:	2023
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DEFORMATION QUANTIZATION; STAR PRODUCTS; CONVERGENCE; FORMALITY Multiple languages Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67277