# Trkalian fields and Radon transformation

Source: [Trkalian fields and Radon transformation](<https://www.sota2.com/research/paper/68fa2e1b1e209131ce85fd82>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:43:49.563Z

Authors: K. Saygili

Published: 2010-03-27T10:56:28.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1003.5287>)

[PDF](<https://arxiv.org/pdf/1003.5287.pdf>)