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Geometric algebra in plasma electrodynamics

Published online by Cambridge University Press:  12 April 2013

D. P. RESENDES
D. P. RESENDES*
Affiliation:
Instituto de Plasmas e Fusão Nuclear (IPFN), Instituto Superior Tècnico (IST), Av. Rovisco Pais, 1, 1049-001, Lisboa, Portugal ([email protected])
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Abstract

Geometric algebra (GA) is a recent broad mathematical framework incorporating synthetic and coordinate geometry, complex variables, quarternions, vector analysis, matrix algebra, spinors, tensors, and differential forms. It has been claimed to be a unified language for physics. GA is presented in the context of the Maxwell-Plasma system. In this formalism the divergence and curl differential operators are united in a single vector derivative, which is invertible, in the form of a first-order Green function. The four Maxwell equations can be combined into a single equation (for homogeneous and constant media) or into two equations involving the invertible vector derivative for more complex media. GA is applied to simple examples to illustrate the compactness of the notation and coordinate-free computations.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Issue 5 , October 2013 , pp. 735 - 738
Copyright
Copyright © Cambridge University Press 2013 

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References

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