Perturbative Bf–yang–mills Theory on Noncommutative R

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. PACS : 11.10. Gh , 10.10. -z , 11.15. q , 11.15. Bt