Quantum space-times and Non-commutative field dynamics

by Dr Timothé Poulain (Laboratoire de Physique Théorique of the Université Paris-Sud (France))

Thursday 7 Dec 2017, 14:30 → 15:30 Europe/Rome

0M03 (Dipartimento di Fisica "Ettore Pancini")

I will discuss implications of the possible quantum nature of space-time on quantum field theories focusing on two examples of Lie algebra-like non-commutative spaces known in the physics literature as $\mathbb{R}^3_\theta$ and (4-dim) $\kappa$-Minkowski. Construction of star products taking advantage of group algebraic structures underlying those quantum spaces will be discussed. Finally, explicit one-loop order corrections to the 2-point function for (real and complex) scalar field theories with quartic interactions will be presented and both UV and IR behaviours as well as UV/IR mixing will be studied.\\ In the $\mathbb{R}^3_\theta$ case functional action will be built taking advantage of star product related to the Kontsevich product and using the usual Laplacian for $\mathbb{R}^3$ as kinetic operator. For $\kappa$-Minkowski, the action will be constructed using kinetic operator related to the Casimir of the $\kappa$-Poincaré algebra and insisting on the preservation of $\kappa$-Poincaré invariance. As we will show, in that latter approach, twists together with KMS condition play an essential role and make possible actual perturbative computations without resorting on closed star product.