Content area
Abstract
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 \(\theta\). 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.
Details
Title
Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map
Author
Bichl, A A 1 ; Grimstrup, J M 1 ; Grosse, H 2 ; Kraus, E 3 ; Popp, L 1 ; Schweda, M 1 ; Wulkenhaar, R 2
1 Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040 Wien, Austria , AT
2 Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria , AT
3 Physikalisches Institut der Universität Bonn, Nußallee 12, 53115 Bonn, Germany , DE
1 Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040 Wien, Austria , AT
2 Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria , AT
3 Physikalisches Institut der Universität Bonn, Nußallee 12, 53115 Bonn, Germany , DE
Pages
165-176
Publication year
2002
Publication date
May 2002
ISSN
14346044
e-ISSN
14346052
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2293985250
Copyright
The European Physical Journal C - Particles and Fields is a copyright of Springer, (2002). All Rights Reserved.