On the derivation of the Dirac Equation

2009/03/23 by R. Sartor, Sartor, R. · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Dirac (video compression format) #Dirac algebra #Dirac equation #FOS: Physical sciences #Mathematical physics #Mathematics #Physics #Quantum Physics (quant-ph) #Quantum mechanics #quant-ph

paper · pdf · doi:10.48550/arxiv.0903.3828

published in arXiv (Cornell University) (Cornell University) · 10 pages

arxiv created 2009/03/23 · openalex publication_date 2009/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We point out that the anticommutation properties of the Dirac matrices can be derived without squaring the Dirac hamiltonian, that is, without explicit reference to the Klein-Gordon equation. We only require the Dirac equation to admit two linearly independent plane wave solutions with positive energy for all momenta. The necessity of negative energies as well as the trace and determinant properties of the Dirac matrices are also a direct consequence of this simple and minimal requirement.

Citations

• The quantum theory of the electron

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