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


Müller-Bahns, Michael ; Neumaier, Nikolai Alexander


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URL: http://ub-madoc.bib.uni-mannheim.de/1733
URN: urn:nbn:de:bsz:180-madoc-17331
Document Type: Working paper
Year of publication: 2003
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
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.
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Müller-Bahns, Michael ; Neumaier, Nikolai Alexander (2003) Invariant Star Products of Wick Type : Classification and Quantum Momentum Mappings. Open Access [Working paper]
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