How do you define a non-perturbative Quantum field theory. What does it mean? I was just digging around some math about the meaning of $Z_1$, and such in terms of probabilities. It turns out these and associated counter terms are derived via perturbation theory. So the question is , if you associate meaning to things like probability of self interaction and such, how do you make these things make sense if you are working non-perturbatively. What is a self interaction outside of perturbation theory?
I mean considering some probable sketch, for some arbitrary calculations , something looking like the lines below might appear, then some cleaver physics is said.
$1 + \Sigma_a$
$\Gamma^{n} \rightarrow Z_{b} \bar{\Gamma^{m}}$
ok so what is a self interaction in non-pertubative models like.
Is a non-pertubative model real? Can it make sense. . . . I don't know .. . . . .
