Relativistic Bound States

Abstract

In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger representation, and similarity transformation methods for Hamiltonian approaches in light-front quantization. Finally, I will comment on a related similarity transformation in the usual equal-time quantized theory.Comment: 9 pages, LaTeX, 3 pspicture diagrams, 3 postscript figures, uses aipxfm.sty. Talk delivered at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 200

Renormalization Group Theory

“…By developing an RG methodology for calculating Regge trajectories then, given the relationship between such trajectories and the existence of bound states in a field theory, it has been possible to use the RG in this extreme asymmetric limit to calculate properties of bound states [28,29]. In [28] different charge sectors of a scalar theory with interaction φ † φ ψ were considered and found to have a surprisingly rich bound state spectrum.…”

Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem

“…The most common one is the ladder approximation which nearly has become synonymous with the Bethe-Salpeter equation although it has numerous deficiencies. [2] Over the years three-dimensional reductions, spectator approximations, light front methods [3]-to name just a few variants -have been investigated and frequently used. In hadronic physics where the perturbative methods of bound-state QED [4] are of little value there is an urgent need for methods which also work at strong coupling.…”