30 research outputs found
Parametric representation of a translation-invariant renormalizable noncommutative model
We construct here the parametric representation of a translation-invariant
renormalizable scalar model on the noncommutative Moyal space of even dimension
. This representation of the Feynman amplitudes is based on some integral
form of the noncommutative propagator. All types of graphs (planar and
non-planar) are analyzed. The r\^ole played by noncommutativity is explicitly
shown. This parametric representation established allows to calculate the power
counting of the model. Furthermore, the space dimension is just a parameter
in the formulas obtained. This paves the road for the dimensional
regularization of this noncommutative model.Comment: 20 pages, 11 figures; the power counting dependence on the graph
genus has been explicitly found; several misprints have been corrected;
version accepted for publication to J. Phys. A: Math. Theo
Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory
We show that the simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is
asymptotically safe to all orders in perturbation theor
Commutative limit of a renormalizable noncommutative model
Renormalizable models on Moyal space have been obtained by
modifying the commutative propagator. But these models have a divergent "naive"
commutative limit. We explain here how to obtain a coherent such commutative
limit for a recently proposed translation-invariant model. The mechanism relies
on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte
One-loop functions of a translation-invariant renormalizable noncommutative scalar model
Recently, a new type of renormalizable scalar model on
the Moyal space was proved to be perturbatively renormalizable. It is
translation-invariant and introduces in the action a term. We
calculate here the and functions at one-loop level for this
model. The coupling constant function is proved to have the
same behaviour as the one of the model on the commutative
. The function of the new parameter is also
calculated. Some interpretation of these results are done.Comment: 13 pages, 3 figure
Overview of the parametric representation of renormalizable non-commutative field theory
We review here the parametric representation of Feynman amplitudes of
renormalizable non-commutative quantum field models.Comment: 10 pages, 3 figures, to be published in "Journal of Physics:
Conference Series
EPRL/FK Group Field Theory
The purpose of this short note is to clarify the Group Field Theory vertex
and propagators corresponding to the EPRL/FK spin foam models and to detail the
subtraction of leading divergences of the model.Comment: 20 pages, 2 figure
Generalization of the Bollob\'as-Riordan polynomial for tensor graphs
Tensor models are used nowadays for implementing a fundamental theory of
quantum gravity. We define here a polynomial encoding the
supplementary topological information. This polynomial is a natural
generalization of the Bollob\'as-Riordan polynomial (used to characterize
matrix graphs) and is different of the Gur\uau polynomial, (R. Gur\uau,
"Topological Graph Polynomials in Colored Group Field Theory", Annales Henri
Poincare {\bf 11}, 565-584 (2010)) defined for a particular class of tensor
graphs, the colorable ones. The polynomial is defined for both
colorable and non-colorable graphs and it is proved to satisfy the
contraction/deletion relation. A non-trivial example of a non-colorable graphs
is analyzed.Comment: 22 pages, 20 figure
A translation-invariant renormalizable non-commutative scalar model
In this paper we propose a translation-invariant scalar model on the Moyal
space. We prove that this model does not suffer from the UV/IR mixing and we
establish its renormalizability to all orders in perturbation theory.Comment: 17 pages, 3 figure
On the Effective Action of Noncommutative Yang-Mills Theory
We compute here the Yang-Mills effective action on Moyal space by integrating
over the scalar fields in a noncommutative scalar field theory with harmonic
term, minimally coupled to an external gauge potential. We also explain the
special regularisation scheme chosen here and give some links to the Schwinger
parametric representation. Finally, we discuss the results obtained: a
noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference
on Noncommutative Geometry and Physics", April 2007, Orsay (France). To
appear in J. Phys. Conf. Se