M. Schweda

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 U(1) gauge theory on with oscillator term and BRST symmetry

Inspired by the renormalizability of the non-commutative Φ4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.

Translation-invariant models for non-commutative gauge fields

Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field [1], we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing.

Space/time non-commutative field theories and causality

Abstract. As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naïve path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative

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

\phi^4

On the Problem of Renormalizability in Non-Commutative Gauge Field Models: A Critical Review

theory. Although in all intermediate steps only three-momenta play a rôle, the final result is manifestly Lorentz covariant and agrees with the naïve calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only.

General solution of the supersymmetry consistency conditions

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

Some supersymmetric aspects of the supertransformation of Becchi, Rouet and Stora

\theta

Perturbative Chern-Simons theory on noncommutative Bbb R3

. 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.