A pedagogical and self-contained introduction to noncommutative quantum field theory is
presented, with emphasis on those properties that are intimately tied to string theory and …

We prove that the real four-dimensional Euclidean noncommutative ϕ 4-model is
renormalisable to all orders in perturbation theory. Compared with the commutative case …

We review the structures imposed on perturbative QFT by the fact that its Feynman diagrams
provide Hopf and Lie algebras. We emphasize the role which the Hopf algebra plays in …

Noncommutative geometry, inspired by quantum physics, describes singular spaces by their
noncommutative coordinate algebras and metric structures by Dirac-like operators. Such …

As a first application of our renormalisation group approach to non-local matrix models [1],
we prove (super-) renormalisability of euclidean two-dimensional noncommutative ϕ 4 …

A non-commutative version of the usual electro-weak theory is constructed. We discuss how
to overcome the two major problems:(1) although we can have non-commutative U …

Solving the exact renormalisation group equation à la Wilson-Polchinski perturbatively, we
derive a power-counting theorem for general matrix models with arbitrarily non-local …

We present the exact solution of a scalar field theory defined with noncommuting position
and momentum variables. The model describes charged particles in a uniform magnetic …

A new version of scale analysis and renormalization theory has been found on the non-
commutative Moyal space. It could be useful for physics beyond the standard model or for …

In this paper we give a much more efficient proof that the real Euclidean ϕ 4-model on the
four-dimensional Moyal plane is renormalisable to all orders. We prove rigorous bounds on …