Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Stationary BPS solutions to dilaton-axion gravity

Stationary four-dimensional BPS solutions to gravity coupled bosonic theories admitting a three-dimensional sigma-model representation on coset spaces are interpreted as null geodesics of the target manifold equipped with a certain number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such geodesics can be directly parametrized in terms of charges saturating the Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of related coset matrices. We investigate in detail the ``dilaton-axion gravity'' with one vector field, and show that in the space of BPS solutions an $SO(1,2) \times SO(2)$ classical symmetry is acting. Within the present formalism the most general multicenter (IWP/Taub-NUT dyon) solutions are derived in a simple way. We also discover a large new class of asymptotically flat solutions for which the dilaton and axion charges are constrained only by the BPS bound. The string metrics for these solutions are generically regular. Both the IWP class and the new class contain massless solutions.Comment: 29 pages, Latex, no figures. To be published in Phys. Rev. D. Minor grammatical and bibliographical change