Four-dimensional quantum field theory suffers from infrared and ultraviolet divergences as well as from the divergence of the renormalised perturbation expansion. Despite early suggestions as to modify the space-time structure [1], quantum field theory on non-commutative spaces was studied in details only after Alain Connes developed noncommutative geometry [2]. The first steps were connected t...

A quantum deformation of the conformal algebra of the Minkowskian spacetime in (3 + 1) dimensions is identified with a deformation of the (4 + 1)-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known κ-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian sp...

We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant,...

A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups are the natural generalization of the notion of a tensor operator for usual groups and that the quantum group coactions induce semigroups of transformations ...

Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of co...

We compute the shear viscosity of the non-commutative N=4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/...