Physics – Mathematical Physics
Scientific paper
2010-03-27
J. Math. Phys. 51, 033513 (2010)
Physics
Mathematical Physics
23 pages
Scientific paper
10.1063/1.3293982
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.
No associations
LandOfFree
Trkalian fields and Radon transformation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trkalian fields and Radon transformation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trkalian fields and Radon transformation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-275507