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Trkalian fields and Radon transformation

Saygili, K.

Journal of mathematical physics, 2010-03, Vol.51 (3), p.033513-033513-24 [Periódico revisado por pares]

Melville, NY: American Institute of Physics

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  • Título:
    Trkalian fields and Radon transformation
  • Autor: Saygili, K.
  • Assuntos: Eigenvalues ; Euclidean space ; Exact sciences and technology ; Knowledge ; Mathematical methods in physics ; Mathematics ; Physics ; Sciences and techniques of general use
  • É parte de: Journal of mathematical physics, 2010-03, Vol.51 (3), p.033513-033513-24
  • Descrição: We write the spherical curl transformation for Trkalian fields using differential forms. Then we consider Radon transform of these fields. The Radon transform of a Trkalian field satisfies a corresponding eigenvalue equation on a sphere in transform space. The field can be reconstructed using knowledge of the Radon transform on a canonical hemisphere. We consider relation of the Radon transformation with Biot–Savart integral operator and discuss its transform introducing Radon–Biot–Savart operator. The Radon transform of a Trkalian field is an eigenvector of this operator. We also present an Ampere-law type relation for these fields. We apply these to Lundquist solution. We present a Chandrasekhar–Kendall-type solution of the corresponding equation in the transform space. Lastly, we focus on the Euclidean topologically massive Abelian gauge theory. The Radon transform of an anti-self-dual field is related by antipodal map on this sphere to the transform of the self-dual field obtained by inverting space coordinates. The Lundquist solution provides an example of quantization of topological mass in this context.
  • Editor: Melville, NY: American Institute of Physics
  • Idioma: Inglês
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