Topologically massive gauge theory: A Lorentzian solution

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space (H) over tilde (3) 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 nu similar to ng(2). 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 pi : (H) over tilde (3) -> (H) over tilde (2)(+) including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of (H) over tilde (3) as a trivial (S) over tilde (1) bundle over the upper portion of the pseudosphere (H) over tilde (2)(+) which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto (H) over tilde (2)(+) using a global section of the solution on (H) over tilde (3). Then we discuss the integration of the field equation using the Archimedes map A : (H) over tilde (2)(+) - {N} -> (C) over tilde (2)(P). We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on (H) over tilde (2)(+)

Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy, and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are the members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor representation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C-3 with an arbitrary function and an exponential factor resulting from this reduction. (C) 2013 AIP Publishing LLC

Topologically massive Abelian gauge theory

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

GINGA OBSERVATIONS OF X1820-303 IN THE GLOBULAR-CLUSTER NGC-6624

We present the first spectral observations obtained by Ginga of the low-mass X-ray binary source X1820-303 located in the globular cluster NGC 6624. Two two-component spectral models are found to provide good fits to the data: a bremsstrahlung component plus a blackbody, or a power law with exponential cut-off plus a blackbody. In both cases, inclusion of an iron line at 6.7 keV improves the fits. After considering the importance of Comptonization for the spectral and temporal behaviour, we select the power law plus blackbody model. This model then provides simple explanations for many of the observed features present in our data. The model requires a scattering cloud surrounding the neutron star, with a Thomson optical depth of approximately 7