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The equivalence theorem and the Bethe-Salpeter equation

S. Kondratyuk·A. D. Lahiff·H. W. Fearing
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Abstract

We solve the Bethe-Salpeter equation for two-particle scattering in a field-theoretical model using two lagrangians related by a field transformation. The kernel of the equation consists of the sum of all tree-level diagrams for each lagrangian. The solutions differ even if all four external particles are put on the mass shell, which implies that observables calculated by solving the Bethe-Salpeter equation depend on the representation of the theory. We point out that this violation of the equivalence theorem has a simple explanation and should be expected for any Bethe-Salpeter equation with a tree-level kernel. Implications for dynamical models of hadronic interactions are discussed.

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S. Kondratyuk, A. D. Lahiff, H. W. Fearing. 2001-10-15. The equivalence theorem and the Bethe-Salpeter equation. https://doi.org/10.1016/s0370-2693(01)01242-4

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