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On the bound state in weakly coupled λ(ϕ6−ϕ4)2

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Abstract

We consider the λ(ϕ6−ϕ4) quantum field theory in two space-time dimensions. Using the Bethe-Salpeter equation, we show that there is a unique two particle bound state if the coupling constant λ>0 is sufficiently small. Ifm is the mass of single particles then the bound state mass is given by

$$_B (\lambda ) = 2m\left( {1 - \frac{9}{8}\left( {\frac{\lambda }{{m^2 }}} \right)} \right)^2 + \mathcal{O}\left( {\lambda ^3 } \right).$$

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References

  1. Bros, J.: Some analyticity properties implied by the two-particle structure of Green's functions in general quantum field theory. In: Analytic Methods in Mathematical Physics (ed. R. Gilbert, R. Newton). New York: Gordon and Breach 1970

    Google Scholar 

  2. Eckmann, J.-P., Epstein, H., Fröhlich, J.: Asymptotic perturbation expansion for theS-matrix and the definition of time ordered functions in relativistic quantum field models. Ann. Inst. H. Poincaré, to appear

  3. Glimm, J., Jaffe, A.: Two and three body equations in quantum field models. Commun. math. Phys.44, 293–320 (1975)

    Google Scholar 

  4. Glimm, J., Jaffe, A., Spencer, T.: The particle structure of the weakly coupledP(ϕ)2 model and other applications of high temperature expansions. In: Constructive Quantum Field Theory (ed. G. Velo, A. Wightman), Lecture Notes in Physics, Vol. 25. Berlin-Heidelberg- New York: Springer 1973

    Google Scholar 

  5. Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in theP(ϕ)2 quantum field model: Ann. Math.100, 585–632 (1974)

    Google Scholar 

  6. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  7. Spencer, T.: The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models: Commun. math. Phys.44, 143–164 (1975)

    Google Scholar 

  8. Spencer, T., Zirilli, F.: Scattering states and bound states in λP(ϕ)2. Commun. math. Phys.49, 1–16 (1976)

    Google Scholar 

  9. Wick, G.C.: Properties of Bethe-Salpeter wave functions. Phys. Rev.96, 1124–1134 (1954)

    Google Scholar 

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Authors and Affiliations

  1. Département de Physique Théorique, Université de Genève, CH-1211, Genève 4, Switzerland

    J. Dimock & J. -P. Eckmann

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  1. J. Dimock
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  2. J. -P. Eckmann
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Communicated by A. S. Wightman

On leave from Department of Mathematics, Suny at Buffalo, USA

Supported by the Fonds National Suisse

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Dimock, J., Eckmann, J.P. On the bound state in weakly coupled λ(ϕ6−ϕ4)2 . Commun.Math. Phys. 51, 41–54 (1976). https://doi.org/10.1007/BF01609050

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