Twistor structures and boost-invariant solutions to field equations
- 22 Downloads
We start with a brief overview of a non-Lagrangian approach to field theory based on a generalization of the Kerr-Penrose theorem and algebraic twistor equations. Explicit algorithms for obtaining the set of fundamental (Maxwell, SL(2,ℂ)-Yang-Mills, spinor Weyl and curvature) fields associated with every solution of the basic system of algebraic equations are presented. The notion of a boost-invariant solution is introduced, and the unique axially-symmetric and boost-invariant solution which can be generated by twistor functions is obtained, together with the associated fields. It is found that this solution possesses a wide variety of point-, string- and membrane-like singularities exhibiting nontrivial dynamics and transmutations.
Unable to display preview. Download preview PDF.
- 1.R. Penrose and W. Rindler, Spinors and Space-Time, vol. 1, 2 (Cambridge University Press, Cambridge, 1984)Google Scholar
- 7.V. V. Kassandrov, in Has the Last Word Been Said on Classical Electrodynamics?, Ed. by A. Chubykalo et al. (Rinton Press, 2004), pp. 42–67; arXiv: physics/0308045.Google Scholar
- 8.Joseph A. Rizcallah, Geometrization of Electromagnetism on the Basis of Spaces with Weyl-Cartan Connections, PhD thesis (RUDN University, Moscow, 1999) [in Russian].Google Scholar
- 9.V. V. Kassandrov and A. V. Tretyakova, Bull. Peoples’ Friend. Univ: Math., Inform., Phys., No. 3, 89 (2009).Google Scholar