Trkalian场与Radon变换
Trkalian fields and Radon transformation
摘要：
我们使用微分形式写出Trkalian场的球面旋度变换。然后考虑这些场的Radon变换。在变换空间中，一个Trkalian场的Radon变换满足球面上相应的本征值方程。可以使用规范半球上的Radon变换的知识来重建场。考虑Radon变换与Biot-Savart积分算子的关系，讨论了Radon-Biot- Savart积分算子的引入对Radon变换的影响。Trkalian域的Radon变换是该算子的特征向量。我们还提出了一个安培定律类型的关系，这些领域。我们将这些应用于Lundquist解决方案。我们在变换空间中给出了相应方程的一个Kendrasekhar-Kendall型解。最后，我们讨论了欧氏拓扑有质量阿贝尔规范理论。反自对偶场的Radon变换通过球面上的对映映射与空间坐标反演得到的自对偶场的变换相联系。伦德奎斯特解提供了一个拓扑质量量子化的例子。
英文摘要：
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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