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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.
Using spinor index notation, the Penrose transform gives a bijection between solutions to the spin / massless field equation ′ ′ ′ ′ = and the first sheaf cohomology group (, ()), where is the Riemann sphere, () are the usual holomorphic line bundles over projective space, and the sheaves under consideration are the sheaves of sections ...
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.
His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory has produced a beautiful and productive approach to the classical equations of mathematical physics. His tilings of the plane underlie the newly discovered quasi-crystals.
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 ...
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 ...
Hints and the solution for today's Wordle on Saturday, February 8.
A spin network, immersed into a manifold, can be used to define a functional on the space of connections on this manifold. One computes holonomies of the connection along every link (closed path) of the graph, determines representation matrices corresponding to every link, multiplies all matrices and intertwiners together, and contracts indices in a prescribed way.