Restoration of rotational symmetry in light-front dynamics

Abstract

Solving the bound state problem in the framework of the light-front dynamics (with the state vector defined in the light-front plane t+z=0), one finds that after truncation - representing approximately the state vector by a finite number of the Fock components, the binding energies become to depend on projection of the angular momentum on the z-axes. This is so called violation of rotational symmetry in light-front dynamics. It is shown that the physical solution is the superposition of these states with some well defined coefficients. For a test, we also solve the Bethe-Salpeter equation and projecting its solution on the light-front, we find the wave functions which do not suffer from violation of the rotation invariance. Comparison with them of solution in the form of superposition shows that not only binding energies but also the wave functions themselves are described by the superpositions of the split states fairly well.