Confining Bethe--Salpeter equation from scalar QCD

Abstract

We give a nonperturbative derivation of the Bethe--Salpeter equation based on the Feynman--Schwinger path integral representation of the one--particle propagator in an external field. We apply the method to the quark--antiquark system in scalar QCD and obtain a confining BS equation assuming the Wilson area law in the straight line approximation. The result is strictly related to the relativistic flux tube model and to the $q\bar{q}$ semirelativistic potential.

Comments: 22 pages, revtex (1 figure appended as uu-encoded file, to include after uncompressing with epsf.sty)