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• W1511532785 abstract "We give a nonperturbative derivation of the Bethe-Salpeter equation in QCD based on the Feynman-Schwinger path integral representation of the one particle propagator in an external field. We obtain a path integral representation for a second order quark-antiquark amplitude in which the gauge field appears only through an appropriate Wilson loop integral $W$. Then, for such a quantity we derive a $qoverline{q}$ BS equation assuming that $imathrm{ln}W$ can be written as the sum of a perturbative contribution and an area term as in the derivation of the heavy quark potential. We also show that, by standard approximations, an effective meson mass operator can be obtained from our BS kernel. From this the corresponding Wilson loop potential is recovered, by $frac{1}{{m}^{2}}$ expansion, spin-dependent and velocity-dependent terms included. On the contrary, neglecting spin-dependent terms, the relativistic flux tube model is reproduced. The method is illustrated also on the simplified case of two spinless particles interacting via a scalar field and on a one-dimensional potential model." @default.
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• W1511532785 date "1996-09-01" @default.
• W1511532785 modified "2023-10-06" @default.
• W1511532785 title "Bethe-Salpeter equation in QCD in a Wilson loop context" @default.
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• W1511532785 doi "https://doi.org/10.1103/physrevd.54.3506" @default.
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