Restoration of rotational symmetry in light-front dynamics

by Prof. V. A. Karmanov* (Lebedev Physical Institute, Moscow, Russia), Prof. E.A. Kupriyanova (Lebedev Physical Institute, Moscow, Russia)

Wednesday Oct 21, 2026, 4:00 PM → 5:30 PM Asia/Shanghai

Solving the bound state problem in the light-front dynamics (LFD), with the state vector defined on the light-front plane $t+z=0$, one finds that the binding energies depend on projection of the angular momentum on the $z$-axis. This nuisance is the price for replacement of the exact Hamiltonian by the approximate -- truncated one. It is so called “violation of rotational symmetry in LFD”. In the explicitly covariant version (with the LF plane $\omega \cdot x = 0$, $\omega^2=0$), energies don’t depend  on the angular momentum projection on the $z$-axis, but depend on projection of the angular momentum on the vector $\vec{\omega}$ determining orientation of the LF plane. In any case, one obtains a set of solutions labeled by this quantum number.

We show 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 solutions on the LF plane, we find “true” LF wave functions which don’t suffer from violation of the rotational invariance. Comparing them with solutions in the form of superposition, we see that the binding energies and the wave functions are described by this superposition fairly well. This restores the rotational symmetry with good precision.

ZOOM ID: 972 4425 2800
PW: 414255

https://zoom.us/j/97244252800?pwd=IoIINT0BNksdIZLdhrQU8sZUL9XEVm.1