Analysis of Helmholtz equation from exterior-algebraic multivector Maxwell fields

Diaz Cilleruelo, Iker

Analysis of Helmholtz equation from exterior-algebraic multivector Maxwell fields

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Diaz Cilleruelo, I. Analysis of Helmholtz equation from exterior-algebraic multivector Maxwell fields. 2021. handle: http://hdl.handle.net/10230/48866

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Abstract

Electromagnetism is one of the pillars of our universe. It represents a base for mostly all modern technologies. It is a well defined and understood theory, that has been proven over the years since its inception. Represented by Maxwell’s equations, it describes the behavior and relations of electrically charged particles and electromagnetic fields. While also describing the propagation of electromagnetic waves. However, the equations are expressed by means of vector algebra, and thus are limited to R 1+3. In this thesis, we reformulate the Maxwell’s equations for (k, n, r) time-space dimensions and multivectors of grade r, by means of exterior algebra. We also derive and analyze the Helmholtz equation, alongside the redefinition of the propagation model in those dimensions. With a last point of focus on data transmission via electromagnetic waves.