Maja Buric

Nonzero Z{yields}{gamma}{gamma} decays in the renormalizable gauge sector of the noncommutative standard model

In this work we propose the Z -> gamma gamma decay as a process strictly forbidden in the standard model, suitable for the search of noncommutativity of coordinates at very short distances. We computed the Z -> gamma gamma partial width in the framework of the recently proposed one-loop renormalizable gauge sector of the noncommutative standard model. New experimental possibilities at LHC are analyzed and a firm bound to the scale of noncommutativity parameter is set around 1 TeV.

The one-loop renormalization of the gauge sector in the θ-expanded noncommutative standard model

In this paper we construct a version of the standard model gauge sector on noncommutative space-time which is one-loop renormalizable to first order in the expansion in the noncommutativity parameter ?. The one-loop renormalizability is obtained by the Seiberg-Witten redefinition of the noncommutative gauge potential for the model containing the usual six representations of matter fields of the first generation.

Renormalizability of noncommutative SU(N) gauge theory

We analyze the renormalizability properties of pure gauge noncommutative SU(N) theory in the θ-expanded approach. We find that the theory is one-loop renormalizable to first order in θ.

Gravity and the structure of noncommutative algebras

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time.

Geometry of the Grosse-Wulkenhaar Model

We analyze properties of a family of finite-matrix spaces obtained by a truncation of the Heisenberg algebra and we show that it has a three-dimensional, noncommutative and curved geometry. Further, we demonstrate that the Heisenberg algebra can be described as a two-dimensional hyperplane embedded in this space. As a consequence of the given construction we show that the Grosse-Wulkenhaar (renormalizable) action can be interpreted as the action for the scalar field on a curved background space. We discuss the generalization to four dimensions.

Non-renormalizability of noncommutative SU(2) gauge theory with fermions

We analyze the divergent part of the one-loop effective action for the noncommutative SU(2) gauge theory coupled to the fermions in the fundamental representation. We show that the divergencies in the 2-point and the 3-point functions in the

Chiral fermions in noncommutative electrodynamics: Renormalizability and dispersion

\theta

Spherically symmetric non-commutative space: d = 4

-linear order can be renormalized, while the divergence in the 4-point fermionic function cannot.

The one-loop effective action for quantum electrodynamics on noncommutative space

We analyze quantization of noncommutative chiral electrodynamics in the enveloping algebra formalism in linear order in noncommutativity parameter {theta}. Calculations show that divergences exist and cannot be removed by ordinary renormalization; however, they can be removed by the Seiberg-Witten redefinition of fields. Performing redefinitions explicitly, we obtain renormalizable Lagrangian and discuss the influence of noncommutativity on field propagation. Noncommutativity affects the propagation of chiral fermions only: half of the fermionic modes become massive and birefringent.

The energy-momentum of a Poisson structure

In order to find a non-commutative analog of Schwarzschild or Schwarzschild–de Sitter black hole we investigate spherically symmetric spaces generated by four non-commutative coordinates in the frame formalism. We present two solutions which, however, do not possess the prescribed commutative limit. Our analysis indicates that the appropriate non-commutative space might be found as a subspace of a higher-dimensional space.