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The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

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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=(x 0,x 1),d 2=2|x 01 +x 02 −x 03 −x 04 |+|x 01 −x 02 |+|x 03 −x 04 | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.

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References

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Author notes

  1. Thomas Spencer

    Present address: Rockefeller University, 10021, New York, N.Y., USA

Authors and Affiliations

  1. Lyman Laboratory, Department of Physics, Harvard University, 02138, Cambridge, Massachusetts, USA

    Thomas Spencer

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  1. Thomas Spencer
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Communicated by A. S. Wightman

Supported in part by the National Science Foundation under Grant MPS 73-05037.

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Spencer, T. The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models. Commun.Math. Phys. 44, 143–164 (1975). https://doi.org/10.1007/BF01608827

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