On the problem of renormalizability in non-commutative gauge field models - a critical review

When considering quantum field theories on non‐commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non‐commutative scalar field theories on four‐dimensional Euclidean Groenewold‐Moyal deformed space, also known as ‘θ‐deformed space’ ℝ4θ. In this work we discuss some major obstacles of constructing a renormalizable non‐commutative gauge field model and sketch some possible ways out. When considering quantum field theories on non‐commutative spaces one inevitably encounters the infamous UV/IR mixing problem. In this work some major obstacles of constructing a renormalizable non‐commutative gauge field model are discussed and some possible ways out are sketched.