Relativistic wave functions and energies for nonzero angular momentum states in light-front dynamics

TL;DR

This paper develops a method within light-front dynamics to construct relativistic wave functions for states with nonzero angular momentum, addressing rotational invariance issues caused by Fock space truncation.

Contribution

It introduces a covariant approach to accurately construct J≠0 states in light-front dynamics, restoring rotational invariance in truncated Fock space calculations.

Findings

Method successfully constructs J≠0 states in covariant LFD.

Restores rotational invariance in truncated Fock space calculations.

Provides exact solutions for nonzero angular momentum states.

Abstract

Light-front dynamics (LFD) is a powerful approach to the theory of relativistic composite systems (hadrons in the quark models and relativistic nucleons in nuclei). Its explicitly covariant version has been recently applied with success to describe the new CEBAF/TJNAF data on the deuteron electromagnetic form factors. The solutions used in were however not obtained from solving exactly the LFD equations but by means of a perturbative calculation with respect to the non relativistic wave function. Since, a consequent effort has been made to obtain exact solutions of LFD equations. The first results concerning J=0 states in a scalar model have been published in nucl-th/9912050. The construction of $J \ne 0$ states in LFD is complicated by the two following facts. First, the generators of the spatial rotations contain interaction and are thus difficult to handle. Second, one is always forced to work in a truncated Fock space, and consequently, the Poincar\'e group commutation relations between the generators -- ensuring the correct properties of the state vector under rotation -- are in practice destroyed. In the standard approach, with the light-front plane defined as $t+z=0$, this violation of rotational invariance manifests by the fact that the energy depends on the angular momentum projection on $z$-axis. We present here a method to construct $J\ne0$ states in the explicitly covariant formulation of LFD and show how it leads to a restoration of rotational invariance.