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The most recent proposal in this direction by Penrose in 2015 was based on noncommutative geometry on twistor space and referred to as palatial twistor theory. [46] The theory is named after Buckingham Palace , where Michael Atiyah [ 47 ] suggested to Penrose the use of a type of " noncommutative algebra ", an important component of the theory.
In physical terms, a spinor should determine a probability amplitude for the quantum state. A manner of regarding the product ψ ϕ as a vector. 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.
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 of ...
The "twistor space" Z is complex projective 3-space CP 3, which is also the Grassmannian Gr 1 (C 4) of lines in 4-dimensional complex space. X = Gr 2 (C 4), the Grassmannian of 2-planes in 4-dimensional complex space. This is a compactification of complex Minkowski space. Y is the flag manifold whose elements correspond to a line in a plane of C 4.
This is standard in twistor theory and supersymmetry. ... Without the indices, i.e. "index free notation", an overbar is retained on right-handed spinor, since ...
By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistor spinors which are also eigenspinors of the Dirac operator. [1] [2] [3] The term is named after Wilhelm Killing.
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 ...
It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory, LQG postulates that the structure of space and time is composed of finite