Perturbative BF-Yang–Mills theory on noncommutative

A U(1) BF-Yang–Mills theory on noncommutative R4 is presented and in this formulation the U(1) Yang–Mills theory on noncommutative R4 is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative R4 is asymptotically free and its UV-behaviour in the computation of the β -function is like the usual SU(N) commutative BFYM and Yang–Mills theories.