Noncommutative Lorentz symmetry and the origin of the Seiberg-Witten map

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.

Note:

20 pages, LaTeX. v2: Streamlined proofs and extended discussion of Lorentz transformations Report-no: TUW 01-019, UWThPh-2001-32

gauge field theory: Yang-Mills
field theory: noncommutative
Seiberg-Witten map
invariance: Lorentz
quantization
symmetry: conformal
Ward identity

References(13)

Figures(0)

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