# Continuity of the four-point function of massive $\varphi_4^4$-theory above threshold

January 30, 2007

In this paper we prove that the four-point function of massive $\varphi_4^4$-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.

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