The shuffle Hopf algebra and quasiplanar Wick products

The operator valued distributions which arise in quantum field theory on the noncommutative Minkowski space can be symbolized by a generalization of chord diagrams, the dotted chord diagrams. In this framework, the combinatorial aspects of quasiplanar Wick products are understood in terms of the shuffle Hopf algebra of dotted chord diagrams, leading to an algebraic characterization of quasiplanar Wick products as a convolution. Moreover, it is shown that the distributions do not provide a weight system for universal knot invariants.Comment: 16 pages, prepared for the conference proceedings "Non commutative Geometry and Physics", Laboratoire de physique th\'eorique d'Orsay, April 23-27, 200

Unitary Quantum Field Theory on the Noncommutative Minkowski space

This is the written version of a talk I gave at the 35th Symposium Ahrenshoop in Berlin, Germany, August 2002. It is an exposition of joint work with S. Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity found in quantum field theory on noncommutative spacetimes in the context of the so-called modified Feynman rules is linked to the notion of time ordering implicitely used in the assumption that perturbation theory may be done in terms of Feynman propagators. Two alternative approaches which do not entail a violation of unitarity are sketched. An outlook upon our more recent work is given.Comment: 6 pages. To appear in the proceedings of 35th International Symposium Ahrenshoop on the theory of Elementary Particles: Recent Developments in String / M Theory and Field Theory, Berlin, Germany, 26-30 Aug 2002 (special issue of the journal "Fortschritte der Physik") v2: minor addition to the abstrac

No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory

In this article we calculate several divergent amplitudes in phi^4-theory on non-commutative space-time in the framework of Interaction Point Time Ordered Perturbation Theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules which allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the lack of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the found Feynman rules this opens promising vistas towards the systematic renormalization of non-commutative field theories.Comment: 23 pages, uses package feynmf, v2: typos, added reference, minor improvement

UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation Theory

In this article an energy correction is calculated in the time independent perturbation setup using a regularised ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes the common quantum field theory on the commutative Minkowski space is reobtained.Comment: 8 pages, 2 figure