# What does that means? "QCD is a non-linear and non-trivial field theory?"

I know QCD is represented by the $$SU(3)$$ group and is non-abelian. Then, as a consequence QCD is a non-linear and non-trivial field theory. I would like to know why? and what does that means?

• perturbation analysis cannot be applied starting from the vacuum modes due to the dimensionless coupling strength constant being much higher than one. Imagine that the physically relevant scenarios and path integrals of vacuum electrodynamics had to be evaluated in electric fields above the Schwinger limit, that is more or less the situation Aug 24 '18 at 13:00
• @lurscher I do not get the definition in this case of non-trivial and non-linear. Sorry. Aug 24 '18 at 13:08
• Are you asking why QCD is non-linear, as in "what is the underlying reason for non-linear effects"? Or do you mean "what is definition of non-linear that is used in QCD"? Aug 24 '18 at 15:12