Noncommutative spacetime symmetries: Twist versus covariance

J. M. Gracia-Bondía, Fedele Lizzi, F. Ruiz Ruiz, and Patrizia Vitale
Phys. Rev. D 74, 025014 – Published 18 July 2006; Erratum Phys. Rev. D 74, 029901 (2006)

Abstract

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an (x,Θ)-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,Θ)-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.

  • Received 5 May 2006
  • Corrected 18 July 2006

DOI:https://doi.org/10.1103/PhysRevD.74.025014

©2006 American Physical Society

Corrections

18 July 2006

Erratum

Publisher’s Note: Noncommutative spacetime symmetries: Twist versus covariance [Phys. Rev. D 74, 025014 (2006)]

J. M. Gracia-Bondía, Fedele Lizzi, F. Ruiz Ruiz, and Patrizia Vitale
Phys. Rev. D 74, 029901 (2006)

Authors & Affiliations

J. M. Gracia-Bondía1, Fedele Lizzi2,*, F. Ruiz Ruiz1,†, and Patrizia Vitale2,‡

  • 1Departamento de Física Teórica I, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 2Dipartimento di Scienze Fisiche, Università di Napoli Federico II, and INFN, Sezione di Napoli, Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

  • *Electronic address: lizzi@na.infn.it
  • Electronic address: ferruiz@fis.ucm.es
  • Electronic address: vitale@na.infn.it

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Issue

Vol. 74, Iss. 2 — 15 July 2006

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