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Communication Dans Un Congrès Année : 2018

Quantum spaces, central extensions of Lie groups and related quantum field theories

Résumé

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed.

Dates et versions

hal-01714772 , version 1 (21-02-2018)

Identifiants

Citer

Timothé Poulain, Jean-Christophe Wallet. Quantum spaces, central extensions of Lie groups and related quantum field theories. 25th International Conference on Integrable Systems and Quantum Symmetries, Jun 2017, Prague, Czech Republic. pp.012032, ⟨10.1088/1742-6596/965/1/012032⟩. ⟨hal-01714772⟩
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