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Are Green functions non-perturbatively infrared finite? In other words imagine one had the final form of the 4-point function for spin-1/2 field, do we still need infrared radiation correction? In other words shouldn't Green functions be finite (non-perturbatively) excluding any bremsstrahlung radiation correction?

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    $\begingroup$ all order in perturbation theory is almost certainly not the same as nonperturbative as perturbation theory probbaly is divergent for nontrivial physical theories like QED or QCD $\endgroup$
    – Yossarian
    Feb 28, 2020 at 16:46
  • $\begingroup$ Yes. Probably the language went abit sloppy! Suppose God has given the final forms of the 4-point function non-Perturbatively, Do we still need IR regularization? $\endgroup$ Feb 29, 2020 at 12:32
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    $\begingroup$ One of the Wightman axioms for QFT is clustering, which is essentially a rigorous statement about the finiteness of the IR limit. $\endgroup$ Mar 2, 2020 at 0:18
  • $\begingroup$ Could you please explain more? $\endgroup$ Mar 2, 2020 at 9:38

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