Publication: Noncommutative spacetime symmetries: Twist versus covariance
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American Physical Society
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 1. We compare our approach with the twist deformed enveloping algebra description of spacetime transformations.
© 2006 The American Physical Society. The authors are grateful to V. Gayral, G. Marmo and C. Moreno for discussions. JMG-B acknowledges support from MEC, Spain, through a ‘Ramón y Cajal’ contract. Partial support from CICyT and UCM-CAM, Spain, through grants No. FIS2005-02309, 910770, and from the ‘‘Progetto di Ricerca di Interesse Nazionale‘‘, Italy, is also acknowledged.
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