September 3, 2020

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Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. Twistor theory was introduced by Roger Penrose from the 1960s as a new approach to the unification of quantum theory with gravity. The idea of twistor theory is that space and time should be described in a completely new way using the geometry of twistor space. Twistor geometry can also describe curved space-times and gravitational degrees of freedom, and since the beginning, there have been attempts to use it to get a quantum theory of gravity. In very general terms, twistor theory consists of the association of a complex space (twistor space) to a real space in a natural and useful way. Starting with a review of the twistor correspondence for four-dimensional … It has the physical interpretation of the space of massless particles with spin. Broadly speaking, twistor theory is a framework for encoding physical information on space-time as geometric data on a complex projective space, known as a twistor space. [2], Degenerate Higher-Order Scalar-Tensor theories, https://en.wikipedia.org/w/index.php?title=Twistor_string_theory&oldid=973812550, Creative Commons Attribution-ShareAlike License, This page was last edited on 19 August 2020, at 10:19. Mathematically, projective twistor space P T {\displaystyle \mathbb {PT} } is a 3-dimensional complex manifold, complex projective 3-space C P 3 {\displaystyle \mathbb {CP} ^{3}}. [2], The most important contribution of twistor string theory has been in the calculation of particle-particle collision scattering amplitudes, which determine the probabilities of the possible scattering processes. Perhaps the new ideas described here, including especially the Euclidean point of view with its breaking of Euclidean rotational invariance, will indicate some new way forward for a twistor-based quantum … By useful, we mean that some important (second order di erential) equations - e.g. But twistor space is chiral (handed) with left- and right-handed objects treated differently. [2], During this period, Edward Witten was a leading developer of string theory. TWISTOR theory is the creation of the great British mathematician and physicist, Professor Sir Roger Penrose, FRS, OM. The one place where the possibility of a connection with spin-network theory remains fairly strong is in twistor diagram theory (Penrose & MacCallum 1972, Penrose 1975a, Sparling 1975, Hodges & Huggett 1980, Hodges 1983, 1984) and in a certain sense it has been SU(2,2) rather than the Poincaré group which has so far replaced SO(3) in the discussion. Twistor theory was introduced by Roger Penrose from the 1960s as a new approach to the unification of quantum theory with gravity. This has allowed both better understanding of experimental observations in particle colliders and deep insights into the natures of different quantum field theories. <> Witten showed that they have a remarkably simple structure in twistor space; in particular amplitudes are supported on algebraic curves. Twistor Theory The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. %PDF-1.3 6 0 obj ��1�'x%4�/ׅ��~r�������1(���2xď]�(*mjDxd��p����q�͞6�q��~8�5�n{��®vx��1�O�Z���u��|��`^$�v�/;���QL!m�4�����%�����mX����z� It is the projectivisation of a 4-dimensional complex vector space, non-projective twistor space T {\displaystyle \mathbb {T} } with a Hermitian form of signature and a holomorphic volume form. Twistor string theory is an equivalence between N = 4 supersymmetric Yang–Mills theory and the perturbative topological B model string theory in twistor space.[1]. x��[[���u~߸�a�d�������-+VdK�֥�0U��bw �F �K�%ݧ/�t�Y�qŪ�lЗs��w.��m]�������=��z�O����x��-?ῶ��?����]�4�����&~�n�S�ڊ��w��Wo����/7�WJ ��=ܼz���wᩫ������wo�kW n����ˬR�г���t�û��/pqk*gj��a6�T\Zs�� � ���_TU-��i�7a��1����?c�����o޾�S�F�Z��6lÌ�j�`�\�5��ih��ڱ������7�~��7����.m���x>|8o���UZӛ�6�E�V�� ��9�dz�܍S?��⎥��~����J� Is a three-dimensional complex projective space in which physical quantities appear as certain structural deformations that space and time be. These lectures from the 1960s as a new approach to the unification of quantum theory with gravity the amplituhedron holomorphic... We explore in these lectures a remarkably simple structure in twistor space ; particular! Physicist, Professor Sir Roger Penrose from the 1960s as a new approach to the unification of quantum with. 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