Twistor (mathematics)

In theoretical and mathematical physics, twistor theory is a theory proposed by Roger Penrose in 1967, as a possible path to a theory of quantum gravity.

In twistor theory, the Penrose transform maps Minkowski space into twistor space, taking the geometric objects from a 4-dimensional space with a Hermitian form of signature (2,2) to geometric objects in twistor space, specified by complex coordinates are called twistors. The twistor approach is especially natural for solving the equations of motion of massless fields of arbitrary spin.

Penrose's twistor theory is unique to four-dimensional Minkowski space, with its signature (3,1) metric. At the heart of twistor theory lies the isomorphism between the conformal group Spin(4,2) and SU(2,2), which is the group of unitary transformations of determinant 1 over a four-dimensional complex vector space that leave invariant a Hermitian form of signature (2,2), see classical group.

${\displaystyle \mathbb {M} ^{c}}$, ${\displaystyle \mathbb {PT} ^{+}}$, ${\displaystyle \mathbb {PN} }$ and ${\displaystyle \mathbb {PT} ^{-}}$ are all homogeneous spaces of the conformal group.

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