Twistor theory

[Jack]

What is the twistor theory?

Could you please answer as simply as possible, thanks.

[selfAdjoint]

A mathematical physics theory invented by Penrose based on projective complex n-space. Brilliant, but pretty much a theory in search of an application.

[Jack]

Originally posted by selfAdjoint
A mathematical physics theory invented by Penrose based on projective complex n-space. Brilliant, but pretty much a theory in search of an application.

Thanks selfAdjoint since you are the only person who actually answered the question but I still need an even simpler defenition because I don't understand. For a start what is n-space

[selfAdjoint]

First I'll assume you are familiar with complex numbers. When we think of them in terms of their real and imaginary parts, z = x + iy, we see they span a two-dimensional surface. Each x iy can be mapped to a point (x,y) in Cartesian coordinates.

Still with me?

In spite of this two dimensional representation, mathemeticians think of the complex numbers as forming just one complex dimension. It's a space with a single complex coordinate, (z). You can defined linear functions on it like uz + v where u and v are complex, just by using complex addition and multiplication. So it's a complex vector space, denoted by C.

Now think of the set of triples (say), (z1, z2, z3), where each z can range over all the complex numbers. Using the same methods, we can define a vector structure on this, and it's denoted C3. We don't have to stop at 3, we can do any number dimension. The n-tuples (z1, z2, z3,...,zn) with the induced vector structure form complex n-space Cn.

[rdegraaf]

Links to articles on the internet are collected at:
http://twistor-theory.rdegraaf.nl/index.asp?sND_ID=436182

Also links to online lectures of Roger Penrose can be found at that site.