Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-04-27
Phys.Rev.D74:025014,2006; Erratum-ibid.D74:029901,2006
Physics
High Energy Physics
High Energy Physics - Theory
19 pages in revtex, references added
Scientific paper
10.1103/PhysRevD.74.025014
We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.
Gracia-Bondia Jose M.
Lizzi Fedele
Ruiz Fernando Ruiz
Vitale Patrizia
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