Perturbative BF-Yang–Mills theory on noncommutative

1999/12/31 by H. Benaoum, H. B. Benaoum
Mathematics · Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Commutative property #Computation #Feynman diagram #Formalism (music) #Gauge theory #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantization (signal processing) #Renormalization #Yang–Mills theory #hep-th

paper · pdf · doi:10.1016/s0550-3213(00)00364-3

published as Nucl.Phys. B585 (2000) 554-566 · 15 pages, 4 figures, latex, version to appear in NPB

arxiv created 2000/05/25 · openalex publication_date 2000/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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