L. Popp

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

THE ENERGY–MOMENTUM TENSOR IN NONCOMMUTATIVE GAUGE FIELD MODELS

\theta

The Superfield formalism applied to the noncommutative Wess-Zumino model

. 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.

NONCOMMUTATIVE U(1) SUPER-YANG–MILLS THEORY: PERTURBATIVE SELF-ENERGY CORRECTIONS

We discuss the different possibilities of constructing the various energy–momentum tensors for noncommutative gauge field models. We use Jackiws method in order to get symmetric and gauge invariant stress tensors — at least for commutative gauge field theories. The noncommutative counterparts are analyzed with the same methods. The issues for the noncommutative cases are worked out.

IR singularities in noncommutative perturbative dynamics

We introduce the notion of superoperators on non-commutative 4 and re-investigate in the framework of superfields the non-commutative Wess-Zumino model as a quantum field theory. In a highly efficient manner we are able to confirm the result that this model is renormalizable to all orders.

Noncommutative spin-1/2 representations

The quantization of the noncommutative , U(1) super-Yang–Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, which is a crucial feature of noncommutative supersymmetric field theories.

Deformed QED via Seiberg-Witten map

We analyse the IR singularities that appear in a noncommutative scalar quantum field theory. We demonstrate, with the help of the effective action and an appropriate field redefinition, that no IR singularities appear in the quadratic part at one-loop order. No new degrees of freedom are needed to describe the UV/IR mixing.

The energy-momentum tensor on noncommutative spaces - some pedagogical comments

Abstract. 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