Non Commutative Field Theory on Rank One Symmetric Spaces

TL;DR

This paper explores extending renormalizable quantum field theories from flat Moyal space to non-flat symmetric spaces, aiming to understand their behavior in more general geometric backgrounds.

Contribution

It introduces the initial steps towards formulating non-commutative quantum field theories on rank one symmetric spaces, expanding the scope beyond flat space.

Findings

Preliminary framework for non-commutative field theory on symmetric spaces

Insights into potential finiteness and renormalizability in curved backgrounds

Foundation for future detailed analysis of quantum fields on non-flat geometries

Abstract

Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to non-flat backgrounds such as solvable symmetric spaces.