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Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map |
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| Authors: | AA Bichl JM Grimstrup H Grosse E Kraus L Popp M Schweda R Wulkenhaar |
| Institution: | 1.Institut für Theoretische Physik, Technische Universit?t Wien, Wiedner Hauptstra?e 8–10, 1040 Wien, Austria ,AT;2.Institut für Theoretische Physik, Universit?t Wien, Boltzmanngasse 5, 1090 Wien, Austria ,AT;3.Physikalisches Institut der Universit?t Bonn, Nu?allee 12, 53115 Bonn, Germany ,DE |
| Abstract: | We show that the non-commutative Yang–Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The non-commutative Yang–Mills action is invariant under combined conformal transformations of the Yang–Mills field and of the non-commutativity parameter . 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. Received: 6 November 2001 / Published online: 5 April 2002 |
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