Involutive representations of coordinate algebras and quantum spaces
| Autor: | Jean-Christophe Wallet, Timothé Poulain, Tajron Jurić |
|---|---|
| Přispěvatelé: | Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique d'Orsay [Orsay] ( LPT ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11) |
| Jazyk: | angličtina |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Pure mathematics [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] space: Poisson FOS: Physical sciences plane wave algebra: Lie quantum space 01 natural sciences [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th] group: representation Quantization (physics) non-Commutative Geometry space-Time Symmetries field theories in lower dimensions models of quantum gravity Poisson manifold 0103 physical sciences Simply connected space Lie algebra Models of Quantum Gravity lcsh:Nuclear and particle physics. Atomic energy. Radioactivity 010306 general physics Mathematical Physics noncommutative Physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] 010308 nuclear & particles physics Field Theories in Lower Dimensions Polar decomposition Space-Time Symmetries Lie group Mathematical Physics (math-ph) Noncommutative geometry field theory: scalar High Energy Physics - Theory (hep-th) SU(2) Product (mathematics) Non-Commutative Geometry lcsh:QC770-798 [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] quantization |
| Zdroj: | Journal of High Energy Physics Journal of High Energy Physics, Vol 2017, Iss 7, Pp 1-32 (2017) JHEP JHEP, 2017, 07, pp.116. ⟨10.1007/JHEP07(2017)116⟩ JHEP, 2017, 07, pp.116. 〈10.1007/JHEP07(2017)116〉 Journal of High Energy Physics, Springer, 2017, 07, pp.116. ⟨10.1007/JHEP07(2017)116⟩ |
| ISSN: | 1029-8479 1126-6708 |
| DOI: | 10.1007/jhep07(2017)116 |
| Popis: | We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that the quantized plane waves obtained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for $SU(2)$. Selecting a subfamily of $^*$-representations, we show that the resulting star-product is equivalent to the Kontsevich product for the Poisson manifold dual to the finite dimensional Lie algebra $\mathfrak{su}(2)$. We discuss the results, indicating a way to extend the construction to any semi-simple non simply connected Lie group and present noncommutative scalar field theories which are free from perturbative UV/IR mixing. 29 pages, several paragraphs added, published in JHEP |
| Databáze: | OpenAIRE |
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