1 research outputs found
Trkalian fields and Radon transformation
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.Comment: 23 page