J. M. Grimstrup

Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map

We show that the photon self-energy in quantum electrodynamics on noncommutative 4 is renormalizable to all orders (both in θ and ) when using the Seiberg-Witten map. This is due to the enormous freedom in the Seiberg-Witten map which represents field redefinitions and generates all those gauge invariant terms in the θ-deformed classical action which are necessary to compensate the divergences coming from loop integrations.

PERTURBATIVE ANALYSIS OF THE SEIBERG–WITTEN MAP

We investigate the quantization of the θ-expanded noncommutative U(1) Yang–Mills action, obtained via the Seiberg–Witten map. The one-loop self-energy correction is gauge-independent. In a further paper, hep-th/0104097, we have shown that the loop correction may be renormalized via an unphysical field redefinition.

Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map

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

Quantisation of

\theta

\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.

-expanded non-commutative QED

Abstract. We analyse two new versions of

Perturbative Chern-Simons theory on noncommutative Bbb R3

\theta

THE ENERGY–MOMENTUM TENSOR IN NONCOMMUTATIVE GAUGE FIELD MODELS

-expanded non-commutative quantum electrodynamics up to first order in

The Superfield formalism applied to the noncommutative Wess-Zumino model

\theta

Vector supersymmetry in topological field theories

and first loop order. In the first version we expand the bosonic sector using the Seiberg-Witten map, leaving the fermions unexpanded. In the second version we leave both bosons and fermions unexpanded. The analysis shows that the Seiberg-Witten map is a field redefinition at first order in