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What is the twistor theory?

Could you please answer as simply as possible, thanks.

Could you please answer as simply as possible, thanks.

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- Thread starter Jack
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- #1

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What is the twistor theory?

Could you please answer as simply as possible, thanks.

Could you please answer as simply as possible, thanks.

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selfAdjoint

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Originally posted by selfAdjoint

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

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selfAdjoint

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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**C**^{3}. 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 **C**^{n}.

Still with me?

In spite of this two dimensional representation, mathemeticians think of the complex numbers as forming just

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

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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.

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