Twistor structures and boost-invariant solutions to field equations

TL;DR

This paper explores a non-Lagrangian twistor-based approach to field theory, deriving explicit algorithms for fundamental fields and identifying a unique boost-invariant solution with complex singularities.

Contribution

It introduces a novel algebraic twistor framework for field solutions and constructs a unique axially-symmetric, boost-invariant solution with dynamic singularities.

Findings

Derived explicit algorithms for fundamental field solutions

Identified a unique boost-invariant solution with singularities

Demonstrated complex point, string, and membrane-like singularities

Abstract

We give 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 reviewed. 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.