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# Topologically massive magnetic monopoles

Classical and Quantum Gravity (Impact Factor: 3.17). 05/2000; 17(19). DOI: 10.1088/0264-9381/17/19/310

Source: arXiv

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**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. Comment: 23 pagesJournal of Mathematical Physics 03/2010; 51(3). DOI:10.1063/1.3293982 · 1.24 Impact Factor -
##### Article: Magnetic Monopole Bibliography-II

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**ABSTRACT:**The bibliography compilation on magnetic monopoles is updated to include references from 2000 till mid 2011. It is intended to contain all experimental papers on the subject and only the theoretical papers which have specific experimental implications. - [Show abstract] [Hide abstract]

**ABSTRACT:**We discuss three mathematical structures which arise in topologically massive Abelian gauge theory. First, the Euclidean topologically massive Abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the Euclidean theory in Cartesian coordinates on which are given by (anti)holomorpic functions. The orthogonality relation of contact structures which are determined by the real parts of these complex solutions separates them into two classes: the self-dual and the anti-self-dual solutions. Thirdly, we apply the curl transformation to this theory. An arbitrary solution is given by a vector tangent to a sphere whose radius is determined by the topological mass in transform space. Meanwhile a gauge transformation corresponds to a vector normal to this sphere. We discuss the quantization of topological mass in an example.International Journal of Modern Physics A 01/2012; 23(13). DOI:10.1142/S0217751X08039840 · 1.70 Impact Factor