This survey tries to give a rigorous definition of Euclidean quantum field theory on a fairly
large class of noncommutative geometries, namely nuclear AF Fréchet algebras. After a …

The special theory of relativity and quantum mechanics merge in the key principle of
quantum field theory, the principle of locality. We review some examples of its …

The aim of this review is to present an overview over available models and approaches to
non-commutative gauge theory. Our main focus thereby is on gauge models formulated on …

We review an approach to non-commutative geometry, where models are constructed by
quantisation of the coordinates. In particular we focus on the full DFR model and its …

In previous work we have shown that the (\theta->\infty)-limit of\phi^ 4_4-quantum field
theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we …

We prove that the ground state for the Dirac equation on Minkowski space in static, smooth
external potentials satisfies the Hadamard condition. We show that it follows from a condition …

In this paper the connection between quantum field theories on flat noncommutative space (-
times) in Euclidean and Lorentzian signature is studied for the case that time is still …

A derivation of the space-time expression of the Pauli–Jordan function (PJF) was shown and
a more compact result was obtained. Compared to other derivations, the approach utilizes …

In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview
over quantum field theories on non-commutative Moyal space and renormalization. In …

This paper addresses three topics concerning the quantization of non-commutative field
theories (as defined in terms of the Moyal star product involving a constant tensor describing …