
TL;DR
This paper proposes a Born level approximation in gauge theories like QED and QCD, where bound states are described by classical gauge fields satisfying field equations, potentially providing a foundation for perturbative expansions that incorporate confinement and chiral symmetry breaking.
Contribution
It introduces a Born approximation for gauge theory bound states, using classical gauge fields determined by Gauss' law, to serve as a starting point for perturbative QCD with confinement.
Findings
Born states are bound by classical gauge fields satisfying field equations.
A confining potential emerges from a Poincaré covariant boundary condition.
Classical gauge fields can be Lorentz boosted to describe moving bound states.
Abstract
Bound state poles in the -matrix of perturbative QED are generated by the {\em divergence} of the expansion in . The perturbative corrections are necessarily singular when expanding around free, \order{\alpha^0} and states that have no overlap with finite-sized atomic wave functions. Nevertheless, measurables such as binding energies do have well-behaved expansions in powers of (and ). It is desirable to formulate the concept of "lowest order" for gauge theory bound states such that higher order corrections vanish in the limit. This may allow to determine a lowest order term for QCD hadrons which incorporates essential features such as confinement and chiral symmetry breaking, and thus can serve as the starting point of a useful perturbative expansion. I discuss a "Born" (no loop, lowest order in ) approximation. Born…
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