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Modeling all matter and energy by eigenspinors on S4(1/h)

The Dirac-like equation for photon introduced by Majorana allows us to consider matter and energy in any background in principle by the same Dirac equation shifted by mass but on spheres in general and 4-sphere in particular, the spectrum of the Dirac operator is extremely regular matching the empirically observed energy quantization.  The Dirac equation on $S^4(1/h)$ is:

$i\frac{\partial}{\partial t} \psi - (D-mc^2)\psi = 0$

where $D$ is the Dirac operator.  Let $\psi_{nl}$ be the eigenspinors with eigenvalue $( 2 + n)h$ with $l\le n$ counting multiplicity.  The massless Dirac equation will be satisfied by linear combinations of $\exp(ih (2+n) t) \psi_{nl}$.  The static solutions are simply from the null space of $D-mc^2$ and the other solutions are vibrating modes.  For $S^4(1/h)$ background there are no massless static solutions.  For nonzero eigenvalues $\lambda_k$ there are static solutions whenever $\lambda_k = mc^2$.

If we consider a given mass $m$ which does occur as an eigenvalue of the Dirac — i.e. integer multiple of $h$ of absolute value at least $2h$, then there exist nontrivial static solutions and corresponding $m$ and then one can identify the other solutions as excited states with respect to the ground state and these will be vibrating.

The identification with mass in the above is purely formal, as it is quite possible to use photon frequency as mass even when these do not have actual mass.   But the identification provides a unified model for both massive and massless objects (fermions and photons).