Naslov
Involutive representations of coordinate algebras and quantum spaces

Autori
Jurić, Tajron ; Poulain, Timothé ; Wallet, Jean-Christophe

Izvornik
The Journal of high energy physics (1126-6708) 7 (2017); 116, 32

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
non-Commutative Geometry ; space-Time Symmetries ; field theories in lower dimensions ; models of quantum gravity

Sažetak
We show that su(2) Lie algebras of coordinate operators related to quantum spaces with su(2) noncommutativity can be conveniently represented by SO(3)-covariant poly-differential involutive representations. We show that the quantized plane waves ob-tained 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 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.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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