Antoine Géré

We show that natural noncommutative gauge theory models on $R^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $R^3_\lambda$ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differen...

We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invari...

We consider a class of gauge invariant models on the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$. Focusing on massless models with no linear $A_i$ dependance, we obtain noncommutative gauge models for which the computation of the propagator can be done in a convenient gauge. We find that the infrared singularity of...

Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixe...