Continuity of the four-point function of massive $φ_4^4$-theory above threshold

Details Continuity of the four-point function of massive $φ_4^4$-theory above threshold Continuity of the four-point function of massive $φ_4^4$-theory above threshold

2007-01-30

arxiv.org/abs/math-ph/0701071v2

Rev.Math.Phys.19:725-748,2007

Physics

Mathematical Physics

23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs added

Scientific paper

10.1142/S0129055X07003103

In this paper we prove that the four-point function of massive $\vp_4^4$-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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