Quantum field theory on the degenerate Moyal space

TL;DR

This paper demonstrates the renormalizability of a scalar quantum field theory on a degenerate non-commutative Moyal space, advancing the understanding of quantum fields in non-commutative geometries.

Contribution

It proves all-order renormalizability of a scalar field on degenerate Moyal space with a suitable counterterm, a key step towards non-commutative Minkowski space QFTs.

Findings

Scalar field theory is renormalizable on degenerate Moyal space.

Introduces a counterterm to achieve renormalizability.

Lays groundwork for non-commutative Minkowski space QFTs.

Abstract

We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises several non trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.