Is There a Twistor Matrix Theory Linked to 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outdated, and the author may already know the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outdated, and the author may already know the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?