Exploring Twistor Matrix Theory: A New Perspective on Complex Projective Spaces

[Ayumi]

Hello [Moderator's note: This message may be a bit
outdated, and the author may already know the
answers. LM]

I am a math student that has come across Witten's relatively new
Twistor String Theory. I found the discussions of Twistor projective
space very stimulating, as it seems these are extensions of complex
projective space, e.g., CP^3. There are various constructions of such
projective spaces, including the matrix representation as primitive
idempotent operators. In the case of CP^3, for instance, points can be
obtained as 4x4 complex primitive idempotents (projections onto
one-dimensional subspaces).

Now I was wondering, since CP^3 is a Twistor projective space, which
can be given a matrix representation, does there exist a corresponding
Twistor Matrix Theory? If so, where can I learn more?

Any help and corrections are appreciated. ^^

~Ayu--
Ayumi
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[member 11137]

Hello [Moderator's note: This message may be a bit
outdated, and the author may already know the
answers. LM]

I am a math student that has come across Witten's relatively new
Twistor String Theory. I found the discussions of Twistor projective
space very stimulating, as it seems these are extensions of complex
projective space, e.g., CP^3. There are various constructions of such
projective spaces, including the matrix representation as primitive
idempotent operators. In the case of CP^3, for instance, points can be
obtained as 4x4 complex primitive idempotents (projections onto
one-dimensional subspaces).

Now I was wondering, since CP^3 is a Twistor projective space, which
can be given a matrix representation, does there exist a corresponding
Twistor Matrix Theory? If so, where can I learn more?

Any help and corrections are appreciated. ^^

~Ayu


--
Ayumi
------------------------------------------------------------------------
Ayumi's Profile: https://www.physicsforums.com/forums/member.php?action=getinfo&userid=35380
View this thread: https://www.physicsforums.com/showthread.php?t=85399

With CP3, do you mean complex projective space = Grassmannian manifold G1,3?

 

[Entropia]

Hello Ayumi,

Thank you for your interest in Twistor Matrix Theory. As you correctly pointed out, Twistor projective spaces are extensions of complex projective spaces and can be represented using matrix representations. However, Twistor Matrix Theory is a relatively new and still developing field, so there is not a lot of literature available on it yet.

One good resource for learning more about Twistor Matrix Theory is the work of Edward Witten, who first introduced the concept in 2003. You can find his papers and talks on the subject online. Additionally, there are a few books that touch on the topic, such as "Twistor Geometry and Field Theory" by Roger Penrose and "Twistor Theory: An Approach to the Quantization of Fields and Space-Time" by Lionel Mason and Jonathan P. Hughes.

I hope this helps and good luck in your studies!