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Particles and Fields

Eur. Phys. J. C 24, 491-494 (2002)
DOI: 10.1007/s10052-002-0938-6

Noncommutative spin- 1/2 representations

J.M. Grimstrup1, H. Grosse2, E. Kraus3, L. Popp1, M. Schweda1 and R. Wulkenhaar2

1  Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
2  Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
3  Physikalisches Institut der Universität Bonn, Nußallee 12, 53115 Bonn, Germany

(Received: 5 December 2001 / Published online: 22 May 2002)

In this letter we apply the methods of our previous paper, hep-th/0108045, to noncommutative fermions. We show that the fermions form a spin- 1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations into a field-dependent part and a $\theta$-part implies the Seiberg-Witten differential equations for the fermions.

© Società Italiana di Fisica, Springer-Verlag 2002