Strict Quantization of Polynomial Poisson Structures
| Autor: | Severin Barmeier, Philipp Schmitt |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
convergence
star products FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik Functional Analysis (math.FA) Mathematics - Functional Analysis 53D55 46E25 16S80 Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) ddc:530 Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik ddc:510 formality deformation quantizations Mathematical Physics |
| Zdroj: | Communications in mathematical physics 398 (2023), Nr. 3 Communications in mathematical physics |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-022-04541-4 |
| Popis: | We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on $\mathbb R^d$, 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 $\hbar$, giving strict quantizations on the space of analytic functions on $\mathbb R^d$ with infinite radius of convergence. We also address further questions such as continuity of the classical limit $\hbar \to 0$, 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. 45 pages, final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|