Twistor representation of null two-surfaces

TL;DR

This paper introduces a twistor-based formalism for describing null two-surfaces in 4D Minkowski space-time, providing a reparametrization invariant approach with a new evolution equation.

Contribution

It presents a novel twistor formulation for null two-surfaces that is constraint-free and derives a non-linear evolution equation using Cartan-Penrose spinor formalism.

Findings

Derived a non-linear evolution equation for null two-surfaces.

Provided a twistor description that is reparametrization invariant.

Analyzed a null two-surface as a caustic of a null hypersurface.

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.