Above picture, belongs to this article and titled above, of frames that Sir Roger Penrose wrote in 1999.

Roger Penrose, a professor of mathematics at the University of Oxford in England, pursues an active interest in recreational math which he shared with his father. While most of his work pertains to relativity theory and quantum physics, he is fascinated with a field of geometry known as tessellation, the covering of a surface with tiles of prescribed shapes.

Being reminded of Roger Penrose I am actually going to contribute this blog entry to him, and sources that I had collected.

**Twistor Theory**

The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised.

**Twistor Program**

http://twistor-theory.rdegraaf.nl/index.asp?sND_ID=436182

R. Penrose and M. A. H. MacCallum, Phys. Reports. 6C (1972) p. 241

pages:

242-243,244-245,246-247,248-249,250-251,252-253,254-255,256-257,258-259,260-261,262-263,264-265,266-265,268-269,270-271,272-273,274-275,276-277,278-279,280-281,282-283,284-285,286-287,288-289,290-291,292-293,294-295,296-297,298-299,300-301,302-303,304-305,306-307,308-309,310-311,312-313,314-315,316-317,318-320,320-322,322-324,324-326,326-328,328-330,330-332

or download the unix tar-ball to get all the pages at once. (WinZip is able to unzip this archive)

**Sir Roger Penrose**

**Fedja Hadrovich**

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.

**R. Penrose, F. Hadrovich**

Twistor Theory

Twistor Theory

The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised.

Lecture I

Lecture II

Lecture III

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