Invariant Star Products of Wick Type : Classification and Quantum Momentum Mappings

Müller-Bahns, Michael ; Neumaier, Nikolai Alexander

273_2003_bearb.pdf - Published

Download (864kB)

URN: urn:nbn:de:bsz:180-madoc-17331
Document Type: Working paper
Year of publication: 2003
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 53D55 53D20 81S10 ,
Subject headings (SWD): Deformationsquantisierung , Geometrische Quantisierung
Keywords (English): deformation quantization , star products , quantum momentum mappings , star products of Wick type
Abstract: We extend our investigations on g-invariant Fedosov star products and quantum momentum mappings [22] to star products of Wick type on pseudo-Kähler manifolds. Star products of Wick type can be completely characterized by a local description as given by Karabegov in [16] for star products with separation of variables. We separately treat the action of a Lie group G on C∞(M)[[v]] by (pull-backs with) diffeomorphisms and the action of a Lie algebra g on C∞(M)[[v]] by (Lie derivatives with respect to) vector fields. Within Karabegov's framework, we prove necessary and sufficient conditions for a given star product of Wick type to be invariant in the respective sense. Moreover, our results yield a complete classification of invariant star products of Wick type. We also prove a necessary and sufficient condition for (the Lie derivative with respect to) a vector field to be even a quasi-inner derivation of a given star product of Wick type. We then transfer our former results about quantum momentum mappings for g-invariant Fedosov star products to the case of invariant star products of Wick type.
Additional information:

Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.

Metadata export


+ Search Authors in

+ Download Statistics

Downloads per month over past year

View more statistics

You have found an error? Please let us know about your desired correction here: E-Mail

Actions (login required)

Show item Show item