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In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 [1] as a possible path [2] to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge.
This is an essential feature of Dirac's theory, which ties the spinor formalism to the geometry of physical space. A manner of regarding a spinor as acting upon a vector, by an expression such as ψv ψ. In physical terms, this represents an electric current of Maxwell's electromagnetic theory, or more generally a probability current.
The projective space in question is the twistor space, a geometrical space naturally associated to the original spacetime, and the twistor transform is also geometrically natural in the sense of integral geometry. The Penrose transform is a major component of classical twistor theory.
In mathematics and theoretical physics (especially twistor theory), twistor space is the complex vector space of solutions of the twistor equation ′ =. It was described in the 1960s by Roger Penrose and Malcolm MacCallum. [ 1 ]
They are a key ingredient in the study of spin structures and higher dimensional generalizations of twistor theory, [3] introduced by Roger Penrose in the 1960s. They have been applied to the study of supersymmetric Yang-Mills theory in 10D, [ 4 ] [ 5 ] superstrings , [ 6 ] generalized complex structures [ 7 ] [ 8 ] and parametrizing solutions ...
In 1967, Penrose invented the twistor theory, which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2,2). [ 45 ] [ 46 ] Penrose is well known for his 1974 discovery of Penrose tilings , which are formed from two tiles that can only tile the plane nonperiodically, and are the first ...
This is standard in twistor theory and ... an overbar is retained on right-handed spinor, since ambiguity arises between chirality when no index is indicated ...
The name twisted geometry captures the relation between these additional degrees of freedom and the off-shell presence of torsion in the theory, but also the fact that this classical description can be derived from Twistor theory, by assigning a pair of twistors to each link of the graph, and suitably constraining their helicities and incidence ...