Twistor theory

  • Thread starter Jack
  • Start date
  • #1
Jack
108
0
What is the twistor theory?

Could you please answer as simply as possible, thanks.
 

Answers and Replies

  • #2
selfAdjoint
Staff Emeritus
Gold Member
Dearly Missed
6,852
10
A mathematical physics theory invented by Penrose based on projective complex n-space. Brilliant, but pretty much a theory in search of an application.
 
  • #3
Jack
108
0
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
 
  • #4
selfAdjoint
Staff Emeritus
Gold Member
Dearly Missed
6,852
10
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.
 
Last edited:
  • #5
rdegraaf
1
0

Suggested for: Twistor theory

  • Last Post
2
Replies
40
Views
5K
Replies
6
Views
2K
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
8
Views
4K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
2K
Top