Gluing Non-commutative Twistor Spaces

Abstract

We describe a general procedure, based on Gerstenhaber–Schack complexes, for extending to quantized twistor spaces the Donaldson–Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on non-commutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.

Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

“…Due to these numerical values of dimensionalities in front of the exponent (63) in Formulae ( 29) and (30) the numerical factor λ −1 appears. It should be observed that, contrary to the case of space-time twists ( 16) and (17), in both twistorial twists (29) and (30), the scaling normalization factor is the same.…”

“…Such a view, conceptually attractive, however still faces the basic question of how the appropriate formulation of quantum gravity in the space-time picture would look. On the twistorial side, some first steps towards the construction of twistorial quantum gravity model were provided by Penrose (see also [29]).…”

“…Our aim is to describe some class of quantum-deformed twistors and provide the counterpart of DSR algebra in the noncommutative framework of quantum twistors. It should be recognized here that there are already several interesting papers dealing with quantum deformations of twistors and their geometries (see, e.g., [23][24][25][26][27][28][29]).…”

On the possibility of a real reform in current physics: Penrose and twistor theory

“…To propose a reform in current physics, it is essential that those aspects that are deficient are exposed. An example of the features of quantum mechanics that did not convince Penrose is that it has the ability to contemplate all possibilities 5 . This is, in fact, one of the strengths of quantum mechanics; however, for Penrose this can take on a negative character.…”

“…Penrose differs from Einstein, among many other aspects, in that the former wants to carry out the reform in quantum physics within the scheme of this field, while Einstein spent more than thirty years of his life trying to find an alternative to quantum physics, something that, as is known, he did not achieve 5. In this point Penrose talks about a very specific characteristic, that is, that of the wave function, which, as is known, has the ability to contemplate all possible options.…”