Topologically massive magnetic monopoles

Classical and Quantum Gravity (Impact Factor: 3.1). 05/2000; DOI: 10.1088/0264-9381/17/19/310
Source: arXiv

ABSTRACT We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution.

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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 pages
    Journal of Mathematical Physics 03/2010; 51(3). DOI:10.1063/1.3293982 · 1.18 Impact Factor
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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.
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    ABSTRACT: We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space by means of an SU(1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of as a trivial bundle over the upper portion of the pseudosphere which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto using a global section of the solution on . Then we discuss the integration of the field equation using the Archimedes map . We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on .
    International Journal of Modern Physics A 01/2012; 22(16n17). DOI:10.1142/S0217751X07036361 · 1.09 Impact Factor
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