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Electromagnetism and the Structure of Matter


World Scientific, Singapore, 2008

The classical theory of electromagnetism is entirely revised in this book by proposing a variant of Maxwell equations that allows solitonic solutions (photons). The Lagrangian is the standard one, but it is minimized on a constrained space that enforces the wave packets to follow the rules of geometrical optics. Exact solutions are explicitly shown; this opens a completely new perspective for the study of light wave phenomena. In the framework of general relativity, the equations are written in covariant form. A coupling with the metric is obtained through the Einstein equation, whose solutions are computed exactly in a lot of original situations. Finally, the explicit construction of elementary particles, consisting of rotating photons, is indicated. The results agree qualitatively and quantitatively with what it is actually observed. This opens the path to an understanding of the structure of matter and its properties, also aimed to provide a causal explanation to quantum phenomena.




World-Scientific link

 book review  of  MathSciNet


1. Something is wrong with classical electromagnetism

  • Maxwell equations and wave-fronts
  • Wave-front propagation
  • Fronts from an oscillating dipole
  • Preliminary conclusions

2. First steps towards the new model

  • Modified Maxwell equations
  • Perfect spherical waves
  • Travelling signal packets
  • Lagrangian formulation
  • Free-waves and the eikonal equation
  • Lorentz invariance

3. Interaction of waves with matter

  • Waves bouncing off an obstacle
  • Diffraction phenomena
  • Adding the mechanical terms
  • Properties of the new set of equations

4. The equations in the framework of general relativity

  • Preliminary considerations
  • The energy tensor
  • Unified field equations
  • The divergence of the magnetic field

5. Building matter from fields

  • Adding the pressure tensor
  • On the existence of particle-like solutions
  • Looking for 2-D constrained waves
  • Neutrinos, electrons and protons
  • Connections with a Dirac type equation

6. Final speculative considerations

  • Towards deterministic quantum mechanics
  • Conclusions