On the geometry of prequantization spaces

Zambon, Marco; Zhu, Chenchang

doi:10.1016/j.geomphys.2007.08.003

Cited by 3 publications

(4 citation statements)

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“…Both choices, however, provide a representation of the Lie algebra of Poisson brackets that is an ingredient in the prequantization (see e.g. [177,180,184]). We have, in particular, [X g , X h ] = X {g,h} .…”

Section: First Order Canonical Formalism With a Basic (D+1)formmentioning

confidence: 99%

Canonical approach to the WZNW model

Furlan¹,

Hadjiivanov²,

Todorov³

2014

Preprint

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The chiral Wess-Zumino-Novikov-Witten (WZNW) model provides the simplest class of rational conformal field theories which exhibit a non-abelian braid-group statistics and an associated "quantum symmetry". The canonical derivation of the Poisson-Lie symmetry of the classical chiral WZNW theory (originally studied by Faddeev, Alekseev, Shatashvili and Gawȩdzki, among others) is reviewed along with subsequent work on a covariant quantization of the theory which displays its quantum group symmetry.

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Section: First Order Canonical Formalism With a Basic (D+1)formmentioning

confidence: 99%

Canonical approach to the WZNW model

Furlan¹,

Hadjiivanov²,

Todorov³

2014

Preprint

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“…In fact, the associated bracket on the space of smooth functions on the manifold does not satisfy the Jacobi identity whose failure is controlled by a generalized closed 3-form. Keeping in mind that the Jacobi structures play a central role in the geometric prequantization of Poisson structures [8,42,13], one of the motivations behind the study of twisted Jacobi structures is the likely role that they can play in some geometric prequantization process of twisted Poisson structures.…”

Section: Introductionmentioning

confidence: 99%

On twisted contact groupoids and on integration of twisted Jacobi manifolds

Petalidou¹

2010

Bulletin des Sciences Mathématiques

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We introduce the concept of twisted contact groupoids, as an extension either of contact groupoids or of twisted symplectic ones, and we discuss the integration of twisted Jacobi manifolds by twisted contact groupoids. We also investigate the very close relationships which link homogeneous twisted Poisson manifolds with twisted Jacobi manifolds and homogeneous twisted symplectic groupoids with twisted contact ones. Some examples for each structure are presented. RésuméOn introduit le concept des groupoïdes de contact tordus, comme une extensionà la fois des groupoïdes de contact et des groupoïdes symplectiques tordus, et on discute l' intégration des variétés de Jacobi tordues par groupoïdes de contact tordus. En plus, onétablit quelques relationsétroites qui unissent les variétés de Poisson homogènes tordues avec celles de Jacobi tordues et les groupoïdes homogènes symplectiques tordus avec ceux de contact tordus. Des exemples pour chaque structureétudiée sont présentés.

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“…On the other hand, Dirac-Jacobi structures (called E 1 (M )-Dirac structures in [11]) include both Dirac and Jacobi structures. They naturally appeared in the geometric prequantization of Dirac manifolds [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the precontact groupoid G associated with an integrable Dirac structure L 0 on M is just the prequantization of the presymplectic groupoid G associated with L 0 (that is, the central extension of Lie groupoids M ×S 1 → G → G satisfying some compatibility conditions), provided that the canonical Dirac Jacobi structure L on M corresponding L 0 is integrable, see Section 5.2. We should mention that M. Zambon and C. Zhu independently study the geometry of prequantization spaces [14].…”

Section: Introductionmentioning

confidence: 99%