Convergence Theorem for Non-commutative Feynman Graphs and Renormalization

TL;DR

This paper provides a rigorous proof of a convergence theorem for Feynman graphs in non-commutative quantum field theories, classifies divergent graphs, and demonstrates renormalizability of certain theories.

Contribution

It offers the first rigorous proof of convergence for Feynman graphs in non-commutative QFT and classifies divergences, advancing understanding of renormalization in these theories.

Findings

Proved convergence theorem for non-commutative Feynman graphs

Classified divergent graphs in massive NQFT

Showed renormalizability of specific NQFT models

Abstract

We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT and demonstrate the renormalizability of some of these theories.