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You had the strange situation where formally accurate models came around in the 1920s such as with the Dirac equation and the Schroedinger equation and it was unclear that the universe is compact.  So these equations were being interpreted in $\mathbf{R^3}$.  Of course the Dirac operator on $\mathbf{R}^3$ has continuous spectrum.  So quantum mechanics produced a bizarre theory that was constructed to force the right equations in the wrong geometry to behave as though it was in the right (compact) geometry.  There are no eigenspinors of the Dirac operator on $\mathbf{R}^3$.  This is well-known in spectral theory of unbounded operators.  So solutions of the Dirac equation of $\mathbf{R}^3$ are not obviously interpretable in terms of localized particles.  You don’t need a bizarre interpretation in a compact manifold, where the Dirac operator has a discrete spectrum.  In fact the eigenspinors of the Dirac operator on $S^3$ are quite localized.  To me they seem similar to wavelets.  Quantum mechanics is a crazy theory which needs to be re-examined by a global approach that is geometric.  Our universe is a hypersurface of a four-sphere with radius $1/h$ which is what forces quantization of energy in the first place.  The Dirac eigenspinors are models of particles without strange assumptions because they are automatically localized objects.  The Dirac equation can be handled using eigenspinors by the simple well-known method: given the eigenspinors solutions of the wave equation is elementary and easy to interpret.