Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map

Details Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map

2001-08-07

arxiv.org/abs/hep-th/0108045v2

Eur.Phys.J.C24:165-176,2002

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX. v2: Streamlined proofs and extended discussion of Lorentz transformations

Scientific paper

10.1007/s100520100857

We show that the noncommutative Yang-Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The noncommutative Yang-Mills action is invariant under combined conformal transformations of the Yang-Mills field and of the noncommutativity parameter \theta. The Seiberg-Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action.

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