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Twistor representation of null two-surfaces

Kostyantin Ilyenko
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Abstract

We present a twistor description for null two-surfaces (null strings) in 4D Minkowski space-time. The Lagrangian density for a variational principle is taken as a surface-forming null bivector. The proposed formulation is reparametrization invariant and free of any algebraic and differential constraints. The spinor formalism of Cartan-Penrose allows us to derive a non-linear evolution equation for the world-sheet coordinate. An example of null two-surface given by the two-dimensional self-intersection (caustic) of a null hypersurface is studied.

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Kostyantin Ilyenko. 2001-09-05. Twistor representation of null two-surfaces. https://doi.org/10.1063/1.1501166

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