On representations of star product algebras over cotangent spaces on Hermitian line bundles
| dc.creator | Bordemann, Martin | |
| dc.creator | Neumaier, Nikolai | |
| dc.creator | Pflaum, Markus J. | |
| dc.creator | Waldmann, Stefan | |
| dc.date | 1998-11-09 | |
| dc.date | 1998-12-17 | |
| dc.date.accessioned | 2026-07-07T05:26:47Z | |
| dc.date.available | 2026-07-07T05:26:47Z | |
| dc.description | For every formal power series $B=B_0 + λB_1 + O(λ^2)$ of closed two-forms on a manifold $Q$ and every value of an ordering parameter $κ\in [0,1]$ we construct a concrete star product $\star^B_κ$ on the cotangent bundle $π: T^*Q\to Q$. The star product $\star^B_κ$ is associated to the formal symplectic form on $T^*Q$ given by the sum of the canonical symplectic form $ω$ and the pull-back of $B$ to $T^*Q$. Deligne's characteristic class of $\star^B_κ$ is calculated and shown to coincide with the formal de Rham cohomology class of $π^*B$ divided by $\imλ$. Therefore, every star product on $T^*Q$ corresponding to the Poisson bracket induced by the symplectic form $ω+ π^*B_0$ is equivalent to some $\star^B_kappa$. It turns out that every $\star^B_kappa$ is strongly closed. In this paper we also construct and classify explicitly formal representations of the deformed algebra as well as operator representations given by a certain global symbol calculus for pseudodifferential operators on $Q$. Moreover, we show that the latter operator representations induce the formal representations by a certain Taylor expansion. We thereby obtain a compact formula for the WKB expansion. | |
| dc.description | LaTeX2e, 38 pages, slight generalization of Theorem 4.4, minor typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/9811055 | |
| dc.identifier | http://arxiv.org/abs/math/9811055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77681 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Functional Analysis | |
| dc.subject | Symplectic Geometry | |
| dc.title | On representations of star product algebras over cotangent spaces on Hermitian line bundles | |
| dc.type | text |