Twistor theory

In theoretical and mathematical physics, twistor theory maps the geometric objects of conventional 3+1 space-time (Minkowski space) into geometric objects in a 4-dimensional space with a Hermitian form of signature (2,2). This space is called twistor space, and its complex valued coordinates are called "twistors."

Twistor theory was first proposed by Roger Penrose in 1967, as a possible path to a theory of quantum gravity. 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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