j,
m_j)\rangle.$$ Here $\mathsf P$ and $\mathsf C$ are the parity and charge conjugation quantum numbers, respectively; and $P=(P^-, P^+, P^1, P^2)$ is the total 4-momentum of the particle, $\widetilde P = (P^-, P^+, -P^1, P^2)$. $\bar h$ represents the antiparticle of hadron $h$.

Particles are further classified by the eigenvalues of the intrinsic angular momenta $\{\vec{\mathcal J}^2,
\mathcal J_z \}$, viz $$\vec{\mathcal J}^2 |\psi_h(P, j, m_j)\rangle = j(j+1) |\psi_h(P, j, m_j)\rangle, \quad
 \mathcal J_z |\psi_h(P, j, m_j)\rangle = m_j |\psi_h(P, j, m_j)\rangle.$$ On the light front, $\vec{\mathcal J}^2$ is dynamical and, in principle, it should be diagonalized simultaneously with the light-front Hamiltonian operator $P^-$ to obtain the total angular momentum $j$ [@Brodsky:1997de]. Accordingly, in a truncated and regularized model space, $\vec{\mathcal
J}^2$ may not commute with $P^-$, and the rotational symmetry is only approximate (see Fig. \[fig:raw\_spectrum\]). To extract $j$, we compute the mass eigenvalues from all $m_j$ sectors. We count the multiplicity of the nearly-degenerate mass eigenstates with the further help of the mirror parity, charge conjugation and other relevant quantities[^4]. For this scheme to succeed, the degeneracies have to be observed in the results with sufficient accuracy to resolve ambiguities.

Basis Representation {#sec:3.1}
--------------------

The eigenvalue equation 