Topologically massive Abelian gauge theory
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, vol.23, no.13, pp.2015-2035, 2008 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 23 Issue: 13
- Publication Date: 2008
- Doi Number: 10.1142/s0217751x08039840
- Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS A
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2015-2035
- Istanbul University Affiliated: Yes
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, IN 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 R-3 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.