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

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dc.creatorMueller-Bahns, Michael F.
dc.creatorNeumaier, Nikolai
dc.date2003-07-24
dc.date2004-02-03
dc.date.accessioned2026-07-07T04:59:52Z
dc.date.available2026-07-07T04:59:52Z
dc.descriptionWe extend our investigations on $\mathfrak g$-invariant Fedosov star products and quantum momentum mappings \cite{MN03a} 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 \cite{Kar96} for star products with separation of variables. We separately treat the action of a Lie group $G$ on $\Cinf{M}[[ν]]$ by (pull-backs with) diffeomorphisms and the action of a Lie algebra $\mathfrak g$ on $\Cinf{M}[[ν]]$ 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 $\mathfrak g$-invariant Fedosov star products to the case of invariant star products of Wick type.
dc.descriptionadditional comments and examples added
dc.identifierhttps://arxiv.org/abs/math/0307324
dc.identifierhttp://arxiv.org/abs/math/0307324
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68164
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject53D55; 53D20
dc.titleInvariant Star Products of Wick Type: Classification and Quantum Momentum Mappings
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