Quantum equations of motion and the geometrical imperative II: relativistic

• URL: http://arxiv.org/abs/2410.21305v1
• Date: Wed, 23 Oct 2024 23:20:10 GMT
• Title: Quantum equations of motion and the geometrical imperative II: relativistic
• Authors: R N Henriksen,
• Abstract summary: We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting $4times 4$ operator represents the square root.
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• Abstract: We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting $4\times 4$ operator $d{\bf S}$ 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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