363 research outputs found
A Remark on the Deformation of GNS Representations of *-Algebras
Motivated by deformation quantization we investigate the algebraic GNS
construction of *-representations of deformed *-algebras over ordered rings and
compute their classical limit. The question if a GNS representation can be
deformed leads to the deformation of positive linear functionals. Various
physical examples from deformation quantization like the Bargmann-Fock and the
Schr{\"o}dinger representation as well as KMS functionals are discussed.Comment: LaTeX2e, 8 page
Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-K\"ahler Manilfolds
In this paper we construct star products on a pseudo-K\"ahler manifold
using a modification of the Fedosov method based on a different
fibrewise product similar to the Wick product on . In a first step
we show that this construction is rich enough to obtain star products of every
equivalence class by computing Deligne's characteristic class of these
products. Among these products we uniquely characterize the ones which have the
additional property to be of Wick type which means that the bidifferential
operators describing the star products only differentiate with respect to
holomorphic directions in the first argument and anti-holomorphic directions in
the second argument. These star products are in fact strongly related to star
products with separation of variables introduced and studied by Karabegov. This
characterization gives rise to special conditions on the data that enter the
Fedosov procedure. Moreover, we compare our results that are based on an
obviously coordinate independent construction to those of Karabegov that were
obtained by local considerations and give an independent proof of the fact that
star products of Wick type are in bijection to formal series of closed
two-forms of type on . Using this result we finally succeed in
showing that the given Fedosov construction is universal in the sense that it
yields all star products of Wick type on a pseudo-K\"ahler manifold.Comment: terminology corrected, typos removed, appendix adde
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