Looking at electron, there is singularity of electric field in it - its values seem to tend to infinity, but also directions create topological singularity ...
This picture suggests that maybe we don't need some additional (out of field) entities for particles, but this construction of field itself is the electron - that particles are some characteristic localized constructs of the field, maintaining their structures/properties - are solitons.
Skyrme used such constructions to model mesons/baryons, they automatically give particles masses (rest energy), allows for various number of them because of annihilation/creation, there is corresponding attraction/repelling for opposite/the same ones, they have integer 'quantum numbers' ...
For example here is nice animation of soliton/antisoliton annihilation which released energy gathered in them (mass) as analogue of photons:
Anyway, for a TOE the perfect situation would be finding a field which family of topological soltions corresponds well to the whole particle menagerie with their properties, decays, dynamics ... and which equations became electromagnetism and gravity far from particles (vacuum state).
Extremely simple field: ellipsoid field surprisingly well qualitatively fulfills these requirements - just a field of real symmetric 3*3 (4*4) matrices, which prefers some set of eigenvalues - it can be seen as stress tensor or as less abstract skyrmion model, but with Higgs-like potential (with topologically nontrivial minimum) or as expansion of ellipse field of light polarization concept considered by for example Berry, Dennis ( http://www.phy.bris.ac.uk/groups/theory/th...s_mr_thesis.pdf ).
Rotating ellipse/ellipsoid by 180deg we get the initial situation, so the simplest constructions of such field have spin 1/2, like in this demonstration allowing also to see attraction/repelling caused by minimizing variousness of the field:
In ellipsoid field in 3D we can choose these axes in 3 ways - we get 3 families of spin 1/2 constructs. There can be created charge-like construct on it getting 3 families of leptons (topology says that they need also to have spin). Then we get constructions like mesons, baryons which finally can join into something like nucleus. Qualitatively masses, properties, decay modes are practically exactly like in particle physics.
Far from solitons dynamics becomes 2 sets of Maxwell's equations - for electromagnetism and gravity.
All of it can be basically seen on pictures - they start on 21 page (after motivations for considering solitons) of this presentation:
It is described and derived in 4-5 sections of: http://arxiv.org/abs/0910.2724
I'm going to make simulations some day, but I would be grateful any constructive comments now - this model is very 'strict': we cannot just guess and add new Lagrangian terms as in standard approach - it's quite correct or just wrong: a single real qualitative problem would probably take it to trash ...
What do you generally think of soliton particle models?