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- Twistor_space abstract "In mathematics, twistor space is the complex vector space of solutions of the twistor equation . It was described in the 1960s by Roger Penrose and MacCallum. According to Andrew Hodges, twistor space is useful for conceptualizing the way photons travel through space, using four complex numbers. He also posits that twistor space may aid in understanding the asymmetry of the weak nuclear force.For Minkowski space, denoted , the solutions to the twistor equation are of the formwhere and are two constant Weyl spinors and is a point in Minkowski space. This twistor space is a four-dimensional complex vector space, whose points are denoted by , and with a hermitian formwhich is invariant under the group SU(2,2) which is a quadruple cover of the conformal group C(1,3) of compactified Minkowski spacetime.Points in Minkowski space are related to subspaces of twistor space through the incidence relationThis incidence relation is preserved under an overall re-scaling of the twistor, so usually one works in projective twistor space, denoted PT, which is isomorphic as a complex manifold to .Given a point it is related to a line in projective twistor space where we can see the incidence relation as giving the linear embedding ofa parametrized by .The geometric relation between projective twistor space and complexified compactified Minkowski space is the same as the relation between lines and two-planes in twistor space; more precisely, twistor space isT := C4. It has associated to it the double fibration of flag manifolds P ←μ F ν→ M, whereprojective twistor spaceP := F1(T) = P3(C) = P(C4)compactified complexified Minkowski spaceM := F2(T) = G2(C4) = G2,4(C)the correspondence space between P and MF := F1,2(T)In the above, P stands for projective space, G a Grassmannian, and F a flag manifold. The double fibration gives rise to two correspondences, c := ν . μ−1 and c−1 := μ . ν−1.M is embedded in P5 ~=~ P(Λ2T) by the Plücker embedding and the image is the Klein quadric.".
- Twistor_space wikiPageID "2688710".
- Twistor_space wikiPageRevisionID "600480787".
- Twistor_space hasPhotoCollection Twistor_space.
- Twistor_space subject Category:Complex_manifolds.
- Twistor_space type Artifact100021939.
- Twistor_space type ComplexManifolds.
- Twistor_space type Conduit103089014.
- Twistor_space type Manifold103717750.
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- Twistor_space type Passage103895293.
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- Twistor_space comment "In mathematics, twistor space is the complex vector space of solutions of the twistor equation . It was described in the 1960s by Roger Penrose and MacCallum. According to Andrew Hodges, twistor space is useful for conceptualizing the way photons travel through space, using four complex numbers.".
- Twistor_space label "Twistor space".
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- Twistor_space wasDerivedFrom Twistor_space?oldid=600480787.
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