Electromagnetic energy-momentum equation without tensors: a geometric algebra approach
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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}.
5 pages, no figures. The following article has been submitted to the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp
5 pages, no figures. The following article has been submitted to the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp