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Suppose we are given a rest mass $m_0$ and asked to solve the Dirac equation $(D-ieA-m_0c^2)\psi = 0$  with $A = ( Ze/\sin(t),0,0,0)$ representing the Coulomb potential.  For this note we assume that scaling is done with $1/h$.  We will have for each $n$ the equation
$\lambda_n^3 - m_0c^2\lambda_n^2 - \frac{R}{4}\lambda - (C_n+m_0 c^2R/4) = 0$
where $R = 12h^2$ is the scalar curvature which is a cubic for which there can be at most three roots for $\lambda$.  If none of the three roots match an eigenvalue of the Dirac operator (which for a 4-sphere is $\pm(2+k)h$, the Dirac equation will not have nontrivial solutions.  In particular on the entirety of $S^4(1/h)$ there are severe mass restrictions for the Dirac equation with Coulomb potential.  This type of mass restriction is a consequence of the discreteness of the Dirac spectrum and the specific formula possible for the projection of $A$ onto eigenspaces.
This means that given a particular mass $m_0$, the possible eigenspace of Dirac operator on which the particle can live are at most three.  The wave equation is then solved my multiplication by $\exp(-i \lambda^2 t)$