The twistor equation states that

where the parentheses denote symmetrization, in a Lorentz transformation , primed spinors transform under the conjugate of the transformation for unprimed ones,Einstein summation is used throughout, and denotes the spinor, which is equivalent to the Levi-Civita connection on Minkowski space. The zero rest mass equation can be solved by twistor functions. The solution uses ideas from complex variable theory and cohomology.