Involutive representations of coordinate algebras and quantum spaces (CROSBI ID 244924)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Jurić, Tajron ; Poulain, Timothé ; Wallet, Jean-Christophe
engleski
Involutive representations of coordinate algebras and quantum spaces
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.
non-Commutative Geometry ; space-Time Symmetries ; field theories in lower dimensions ; models of quantum gravity
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Podaci o izdanju
7
2017.
116
32
objavljeno
1126-6708
1029-8479
10.1007/JHEP07(2017)116