Electromagnetic energy-momentum equation without tensors: a geometric algebra approach

2008/07/09 by Quirino M. Sugon, Sugon, Quirino M., Daniel J. McNamara +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Classical Physics (physics.class-ph) #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.0807.1382

openalex publication_date 2008/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of the energy-momentum density. We show that the scalar and vector parts of this equation are the differential conservation laws for energy and momentum, and the imaginary vector part is a relation for the curl of the Poynting vector. We can show that the spacetime derivative of this energy-momentum equation is a wave equation. Our formalism is Dirac-Pauli-Hestenes algebra in the framework of Clifford (Geometric) algebra Cl_4,0.

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