 
Summary: 1
Twistor Primer
By Fedja Hadrovich
Introduction
In the past 30 years, a lot of work has been done on developing twistor theory. Its
creator, Roger Penrose, was first led to the concept of twistors in his investigation of the
structure of spacetime and it was he who first saw the wide range of applications for
this new mathematical construct. Yet 30 years later, twistors remain relatively
unknown even in the mathematical physics community. The reason for this may be the
air of mystery that seems to surround the subject even though it provides a very elegant
formalism for both general relativity and quantum theory. These notes are based on a
graduate lecture course given by R. Penrose in Mathematical Institute, Oxford, in 1997
and should give a brief introduction to the basic definitions. Let us begin with the
building blocks: spinors.
Spinors
Let Ka
be a vector in a + ! ! !( ) spacetime. We choose to represent it in the form of a
Hermitian matrix:
Note that 2 det K A !A
( )= gabKa
