We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

A Translation-Invariant Renormalizable Non-Commutative Scalar Model Page 1 Digital
Object Identifier (DOI) 10.1007/s00220-008-0658-3 Commun. Math. Phys. 287, 275–290 (2009) …

A bstract We consider the noncommutative space\(\mathbb {R} _ {\lambda}^ 3\), a
deformation of the algebra of functions on\({{\mathbb {R}}^ 3}\) which yields a “foliation” …

A bstract We discuss the construction of κ-Poincaré invariant actions for gauge theories on κ-
Minkowski spaces. We consider various classes of untwisted and (bi) twisted differential …

A natural star product for 4-d κ-Minkowski space is used to investigate various classes of κ-
Poincaré invariant scalar field theories with quartic interactions whose commutative limit …

A bstract We consider a family of κ-Poincaré invariant scalar field theories on 4-d κ-
Minkowski space with quartic orientable interaction, that is for which ϕ and its conjugate ϕ† …

We consider a class of gauge-invariant models on the noncommutative space R λ 3, a
deformation of the algebra of functions on R 3. Focusing on massless models with no linear …

A bstract We show that natural noncommutative gauge theory models on\({\mathrm {\mathbb
{R}}} _ {\uplambda}^ 3\) can accommodate gauge invariant harmonic terms, thanks to the …

Derivations of a noncommutative algebra can be used to construct differential calculi, the so-
called derivation-based differential calculi. We apply this framework to a version of the Moyal …

Candidates for renormalizable gauge theory models on Moyal spaces constructed recently
have non-trivial vacua. We show that these models support vacuum states that are invariant …