Abstract

We extend methods of high temperature expansions to show that for even weakly coupledP(ϕ)2 quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x0,x1),d2=2|x10+x20−x30−x40|+|x10−x20|+|x30−x40| and e(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.

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