Journey to the Bound States

Abstract

Guided by the observed properties of hadrons I formulate a perturbative bound state method for QED and QCD. The expansion starts with valence Fock states ($e^+e^-,\ q\bar q,\ qqq,\ gg$) bound by the instantaneous interaction of temporal gauge ($A^0=0$). The method is tested on Positronium atoms at rest and in motion, including hyperfine splitting at $O(\alpha^4)$, electromagnetic form factors and deep inelastic scattering. Relativistic binding is studied for QED in $D=1+1$ dimensions, demonstrating the frame independence of the DIS electron distribution and its sea for $x_{bj} \to 0$. In QCD a homogeneous solution of Gauss' constraint in $D=3+1$ implies $O(\alpha_s^0)$ confining potentials for $q\bar q,\ q\bar qg,\ qqq$ and $gg$ states, whereas $q\bar q\,q\bar q$ is unconfined. Meson states lie on linear Regge trajectories and have the required frame dependence. A scalar bound state with vanishing four-momentum causes spontaneous chiral symmetry breaking when mixed with the vacuum. These lecture notes assume knowledge of field theory methods, but not of bound states. Brief reviews of existing bound state methods and Dirac electron states are included. Solutions to the exercises are given in the Appendix.