Bound states at lowest order in hbar

Details Bound states at lowest order in hbar Bound states at lowest order in hbar

2009-09-16

arxiv.org/abs/0909.3045v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, 4 figures. Minor changes in text, one reference added. Meson solution modified, baryon solution added

Scientific paper

Bound states poles in scattering amplitudes are generated by the divergence of the perturbative series due to enhanced Coulomb scattering near thresholds. This suggests to organize bound state calculations according to an expansion in hbar, i.e., in the number of loops. I study QED and QCD bound states at lowest order in hbar, which are analogous to Born amplitudes. The absence of loops allows the use of retarded boundary conditions where particles only propagate forward in time, making a hamiltonian approach feasible. The instantaneous A^0 field is determined by the equations of motion separately for each Fock component of the bound state. The field equations are compatible with a linear A^0 potential as a homogeneous, non-perturbative solution. Stationarity of the action determines the direction of the ensuing constant electric field in each Fock state. Applying this approach to relativistic qqbar and qqq states in QCD results in a bound state equation which provides a reasonable description of the spectrum, including linear Regge trajectories. The equal-time wave functions have unique Lorentz transformation properties, which ensure the correct dependence of the bound state energy on the center-of-mass momentum. The qqq potential is gauge covariant and confines the three quarks in a symmetric way.

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