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Generalised Maxwell equations in higher dimensions

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Abstract
This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension and their connections with the Rarita-Schwinger equation. This is done using the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the spin group can be realised in terms of polynomials satisfying a system of differential equations. This allows the construction of generalised wave equations in terms of the unique conformally invariant second-order operator acting on harmonic-valued functions. We prove the ellipticity of this operator and use this to investigate the kernel, focusing on both polynomial solutions and the fundamental solution.
Keywords
Spin, Representations, Clifford Analysis, Operators

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MLA
Eelbode, David, and Matthias Roels. “Generalised Maxwell Equations in Higher Dimensions.” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 10, no. 2, SPRINGER BASEL AG, 2016, pp. 267–93, doi:10.1007/s11785-014-0436-5.
APA
Eelbode, D., & Roels, M. (2016). Generalised Maxwell equations in higher dimensions. COMPLEX ANALYSIS AND OPERATOR THEORY, 10(2), 267–293. https://doi.org/10.1007/s11785-014-0436-5
Chicago author-date
Eelbode, David, and Matthias Roels. 2016. “Generalised Maxwell Equations in Higher Dimensions.” COMPLEX ANALYSIS AND OPERATOR THEORY 10 (2): 267–93. https://doi.org/10.1007/s11785-014-0436-5.
Chicago author-date (all authors)
Eelbode, David, and Matthias Roels. 2016. “Generalised Maxwell Equations in Higher Dimensions.” COMPLEX ANALYSIS AND OPERATOR THEORY 10 (2): 267–293. doi:10.1007/s11785-014-0436-5.
Vancouver
1.
Eelbode D, Roels M. Generalised Maxwell equations in higher dimensions. COMPLEX ANALYSIS AND OPERATOR THEORY. 2016;10(2):267–93.
IEEE
[1]
D. Eelbode and M. Roels, “Generalised Maxwell equations in higher dimensions,” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 10, no. 2, pp. 267–293, 2016.
@article{7901978,
  abstract     = {{This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension and their connections with the Rarita-Schwinger equation. This is done using the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the spin group can be realised in terms of polynomials satisfying a system of differential equations. This allows the construction of generalised wave equations in terms of the unique conformally invariant second-order operator acting on harmonic-valued functions. We prove the ellipticity of this operator and use this to investigate the kernel, focusing on both polynomial solutions and the fundamental solution.}},
  author       = {{Eelbode, David and Roels, Matthias}},
  issn         = {{1661-8254}},
  journal      = {{COMPLEX ANALYSIS AND OPERATOR THEORY}},
  keywords     = {{Spin,Representations,Clifford Analysis,Operators}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{267--293}},
  publisher    = {{SPRINGER BASEL AG}},
  title        = {{Generalised Maxwell equations in higher dimensions}},
  url          = {{http://dx.doi.org/10.1007/s11785-014-0436-5}},
  volume       = {{10}},
  year         = {{2016}},
}

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