Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory

Abstract

We consider the general framework of perturbative quantum field theory for the pure Yang-Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs. Next we prove that Wick expansion property can be preserved for all cases in order $ n = 2. $ However, gauge invariance is broken for chronological products of Wick submonomials.