Leveraging Prior Known Vector Green Functions in Solving Perturbed Dirac Equation in Clifford Algebra

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Seagar, Andrew

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Solving boundary value problems with boundary element methods requires specific Green functions suited to the boundary conditions of the problem. Using vector algebra, one often needs to use a Green function for the Helmholtz equation whereas it is a solution of the perturbed Dirac equation that is required for solving electromagnetic problems using Clifford algebra. A wealth of different Green functions of the Helmholtz equation are already documented in the literature. However, perturbed Dirac equation is only solved for the generic case and only its fundamental solution is reported. In this paper, we present a simple framework to use known Green functions of Helmholtz equation to construct the corresponding Green functions of perturbed Dirac equation which are essential in finding the appropriate kernels for integral equations of electromagnetic problems. The procedure is further demonstrated in a few examples.

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Advances in Applied Clifford Algebras

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30

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4

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Â© 2020 Springer Nature Switzerland AG. This is an electronic version of an article published in Advances in Applied Clifford Algebras, 2020, 30 (4), pp. 56. Applied Clifford Algebras is available online at: http://link.springer.com/ with the open URL of your article.

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Pure mathematics

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Physical Sciences

Mathematics, Applied

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Mathematics

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Shahpari, M; Seagar, A, Leveraging Prior Known Vector Green Functions in Solving Perturbed Dirac Equation in Clifford Algebra, Advances in Applied Clifford Algebras, 2020, 30 (4), pp. 56