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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1$\begingroup$ 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 $\endgroup$– YossarianFeb 28, 2020 at 16:46
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$\begingroup$ 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? $\endgroup$– Bastam TajikFeb 29, 2020 at 12:32
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1$\begingroup$ One of the Wightman axioms for QFT is clustering, which is essentially a rigorous statement about the finiteness of the IR limit. $\endgroup$– Prof. LegolasovMar 2, 2020 at 0:18
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$\begingroup$ Could you please explain more? $\endgroup$– Bastam TajikMar 2, 2020 at 9:38