The inverse Penrose transform of a solution to the Maxwell-Dirac-Weyl field equations
The authors present an explicit family of solutions to the nonlinear coupled Maxwell-Dirac-Weyl equations on a Minkowskian space-time. It is shown using results of \textit{G. M. Henkin} and \textit{Yu. Manin} [Phys. Lett. B 95, 405-408 (1980)] that these solutions are equivalent by use of the Penrose transform to a coupled system of cohomology classes and a complex line bundle on the space of null lines in Minkowski space. The inverse Penrose transform is computed and this yields explicit expressions for the line bundle, the obstruction to extension and the two cohomology classes.
scientific article; zbMATH DE number 3879683
scientific article