Twistor Theory (The Penrose Transform)

1982 ◽  
pp. 1-11
Author(s):  
M. G. Eastwood
Keyword(s):  
Twistor Theory ◽  
Penrose Transform

The generalized Penrose-Ward transform

1985 ◽  
Vol 97 (1) ◽  
pp. 165-187 ◽  
Author(s):  
Michael G. Eastwood
Keyword(s):  
Differential Equations ◽  
Twistor Theory ◽  
Field Equations ◽  
Massless Field ◽  
Penrose Transform ◽  
Natural Connection ◽  
Linear Version ◽  
Linear Differential ◽  
Complex Projective ◽  
Special Case

The Penrose transform is an integral geometric method of interpreting elements of various analytic cohomology groups on open subsets of complex projective 3-space as solutions of linear differential equations on the Grassmannian of 2-planes in 4-space. The motivation for such a transform comes from interpreting this Grassmannian as the complexification of the conformal compactification of Minkowski space, the differential equations being the massless field equations of various helicities. This transform is a cornerstone of twistor theory [22, 24, 30], but the methods generalize considerably as will be explained in this article. Closely related is the Ward correspondence[28], a non-linear version of a special case of the Penrose transform. It also admits a rather more general treatment. The object of this article is to explain the general case and the natural connection between the Penrose and Ward approaches.

An Introduction to Twistor Theory

1994 ◽  
Author(s):  
S. A. Huggett ◽  
K. P. Tod
Keyword(s):  
Twistor Theory

Integrable hierarchies in twistor theory

1998 ◽  
Author(s):  
Maciej Dunajski
Keyword(s):  
Integrable Hierarchies ◽  
Twistor Theory

scholarly journals Philosophical Aspects of Astrobiology Revisited

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 55
Author(s):  
Rainer E. Zimmermann
Keyword(s):  
Dynamical Systems ◽  
First Principles ◽  
Special Form ◽  
Mathematical Representation ◽  
Dynamical Structure ◽  
Twistor Theory ◽  
Fundamental Physics ◽  
Physical Universe ◽  
The World ◽  
Traditional Sense

Given the idea that Life as we know it is nothing but a special form of a generically underlying dynamical structure within the physical Universe, we try to introduce a concept of Life that is not only derived from first principles of fundamental physics, but also metaphysically based on philosophical assumptions about the foundations of the world. After clarifying the terminology somewhat, especially with a view to differentiating reality from modality, we give an example for a mathematical representation of what the substance of reality (in the traditional sense of metaphysics) could actually mean today, discussing twistor theory as an example. We then concentrate on the points of structural emergence by discussing the emergence of dynamical systems and of Life as we know it, respectively. Some further consequences as they relate to meaning are discussed in the end.

scholarly journals Bulk interactions and boundary dual of higher-spin-charged particles

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Adrian David ◽  
Yasha Neiman
Keyword(s):  
Relative Velocity ◽  
Black Hole Solution ◽  
Vector Model ◽  
Boundary Theory ◽  
Gauge Fields ◽  
Leading Order ◽  
Gravitational Forces ◽  
Penrose Transform ◽  
Higher Spin ◽  
Non Locality

Abstract We consider higher-spin gravity in (Euclidean) AdS4, dual to a free vector model on the 3d boundary. In the bulk theory, we study the linearized version of the Didenko-Vasiliev black hole solution: a particle that couples to the gauge fields of all spins through a BPS-like pattern of charges. We study the interaction between two such particles at leading order. The sum over spins cancels the UV divergences that occur when the two particles are brought close together, for (almost) any value of the relative velocity. This is a higher-spin enhancement of supergravity’s famous feature, the cancellation of the electric and gravitational forces between two BPS particles at rest. In the holographic context, we point out that these “Didenko-Vasiliev particles” are just the bulk duals of bilocal operators in the boundary theory. For this identification, we use the Penrose transform between bulk fields and twistor functions, together with its holographic dual that relates twistor functions to boundary sources. In the resulting picture, the interaction between two Didenko-Vasiliev particles is just a geodesic Witten diagram that calculates the correlator of two boundary bilocals. We speculate on implications for a possible reformulation of the bulk theory, and for its non-locality issues.

scholarly journals The inverse Penrose transform on Riemannian twistor spaces

1997 ◽  
Vol 22 (1) ◽  
pp. 59-76
Author(s):  
Yoshinari Inoue
Keyword(s):  
Twistor Spaces ◽  
Penrose Transform

scholarly journals GL(2, R) STRUCTURES, G2 GEOMETRY AND TWISTOR THEORY

2010 ◽  
Vol 63 (1) ◽  
pp. 101-132 ◽  
Author(s):  
M. Dunajski ◽  
M. Godlinski
Keyword(s):  
Twistor Theory

The Central Programme of Twistor Theory

1999 ◽  
Vol 10 (2-3) ◽  
pp. 581-611 ◽  
Author(s):  
Roger Penrose
Keyword(s):  
Twistor Theory

Twistor theory: An approach to the quantisation of fields and space-time

1973 ◽  
Vol 6 (4) ◽  
pp. 241-315 ◽  
Author(s):  
R. Penrose ◽  
M.A.H. MacCallum
Keyword(s):  
Space Time ◽  
Twistor Theory
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