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Quantum equations of motion and the geometrical imperative II: relativistic

General Physics 2024-10-30 v1 High Energy Physics - Theory Quantum Physics

Abstract

We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting 4×44\times 4 operator dSd{\bf S} that represents the square root, can be used to transform four vectors between relatively moving observers. This effects the usual Lorentz transformation. In addition it acts on a Dirac bi-spinor. The operator is essentially a Hamiltonian that can be used to write an equation of motion for a relativistic spinor. This turns out to be the Dirac equation for electrons in standard form. We believe that is is a new approach to familiar results.

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Cite

@article{arxiv.2410.21305,
  title  = {Quantum equations of motion and the geometrical imperative II: relativistic},
  author = {R N Henriksen},
  journal= {arXiv preprint arXiv:2410.21305},
  year   = {2024}
}

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20 pages no figures