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Questions tagged [twistor]

Twistor theory is an approach to spacetime focused on null (light-like) geodesics, instead of points (events).

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Four-brackets (Hodges, Momentum Twistors)

I use the reference from Andrew Hodges, available at https://arxiv.org/abs/0905.1473. I am having trouble understanding his use of the four-bracket. I refer to equation 6 and equation 9, where he ...
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1answer
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Problems with Twistor theory

Penrose developed a theory called "twistor theory" that tries to describe the universe using twistors. (https://en.wikipedia.org/wiki/Twistor_theory) From what I've read, there are a lot of papers ...
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Intuitively understanding complex projective space or twistor space

I'm studying momentum twistor variables, which I understand can be seen to be defined projectively from dual complexified Minkowski space to this complex projective space $\mathbb{C}\mathbb{P}^3$. ...
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Doesn't backward in time paradox exist in complex 8-space model and others?

Penrose twistors employ complex 4-space. Multiple complex space or multiple time dimensions have been proposed before in theoretical physics. For example there is the 8-space where there is zero ...
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What does Mobius group/transformations have to do with special relativity?

The group of Mobius transformations, denoted by ${\rm Mob}(2,\mathbb{C})$, is isomorphic to ${\rm SL}(2,\mathbb{C}))/\mathbb{Z}_2$ which in turn is isomorphic to the Lorentz group ${\rm SO}^+(3,1)$. ...
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From twistors and supertwistors to hypertwistors and hypersupertwistors

Twistor and supertwistor methods are, currently, a framework for General Relativity, beyond General Relativity and string/brane theories. What are hypertwistors and hypersupertwistors and their ...
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Other spaces like Fourier space

Are there any other spaces like Fourier space in which one can more physical information than configuration space? In a summer school about scattering amplitudes, someone told me that this relation ...
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A question about relations between twistor, entanglement and light ray

In his book 'The road to reality', R. Penrose wrote: It is possible to regard twistor theory as a continuation of the spin network programme to obtain a relativistic scheme, in which idealized light ...
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Question on $E_8$ and twistor space

The Kahler $4$ form constructed from two-forms $\{\alpha, \beta\} \in H^2(M,\mathbb Z)$, and $M$ a $4$-manifold, is induced by $\alpha\wedge\beta$ with the map $H^2(M, \mathbb Z)\otimes H^2(M, \mathbb ...
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Momentum Twistor variables and non-planar theory

I know that the use of twistur-momentum variables makes manifest the arising of certain poles in scattering amplitudes: if the sum of external momenta $P_I = p_i + p_{i+1} + ... + p_j$ is going on-...
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Conformal compactification and the use of spinors (Twistor theory)

I was reading the book from Huggett and Tod "An introduction to twistor theory" and as the book evolves they reach to the necessity to "found" a Lie derivative of a spinor respect to a conformal ...
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Twistor theory. Huggett and Tod (problems with one equation)

I'm reading about twistors from the book of Huggett and Tod: $\textit{ An introduction to twistor theory}$. I'm trying to understand everything and reproduce every equation that comes here. So, ...
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Question about $\alpha-$plane in twistor theory

In twistor theory, given the complexified Minkowski space $CM$ and the projective twistor space $PT$, an $\alpha-$plane is defined as the correspondence in $CM$ wit a point $Z \in PT$. But I found ...
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In twistor theory, what's the relation between points with dual Plucker coordinates? Also about a special null line

In twistor theory, each point $Z=[Z0,Z1,Z2,Z3]$ in the complexified Minkowski space $CM$ has a correspondent Plucker coordinate $P(Z)$ embedded in $CP^5$ and we can also find its dual $P(Z)^{*}$. My ...
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Twistor theory? [closed]

There is a great deal of basic information available about String Theory, but very little about alternative theories such as Twistor theory. Can anyone give me, in layman's terms, an idea of the basic ...
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Timelike Loop Spaces as Projective Null Twistor Spaces

Let $\mathcal{M}$ be a spacetime, and let $\Omega\mathcal{M}$ denote the loop space of the spacetime. My idea is that the set of all closed timelike curves of $\mathcal{M}$ forms the projective null ...
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286 views

Definition and motivation for Twistors

What are Twistors? Why are they important? This particular statement in Wikipedia is intriguing According to Andrew Hodges, twistor space is useful for conceptualizing the way photons travel ...
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Helicity for Zero Rest Mass Field Equations

I'm trying to reconcile the usual definition of the helicity operator, namely $$ h = \hat{p}.S$$ with the definition of a massless helicity $n$ field as a symmetric spinor field $\phi^{A\dots B}$ ...
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Twistor Function for Coulomb Field

In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function $$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$ produces an anti-self-dual ...
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Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?

As explained for example in this article by Prof. Strassler, modern twistor methods to calculate scattering amplitudes have already been proven immensely helpful to calculate the standard model ...
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What happens to string theory if spacetime is doomed?

What is expected to happen with string theory, if physics is reformulated according the lines hinted at by the twistor-uprising business discussed in this question and its answers for example and ...
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Approaches to Quantum gravity [closed]

I'm going to start my graduate studies in theoretical physics. My supervisor wants me to work on quantum gravity. He gave me the liberty to chose a particular approach to Quantum gravity (Excluding ...
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3answers
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Gentle introduction to twistors

When reading about the twistor uprising or trying to follow a corresponding Nima talk, it always annoys me that I have no clue about how twistor space, the twistor formalism, or twistor theory works. ...
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MVH amplitudes and the unitarity method

In the last 5 years there has been a silent revolution in QFT called the unitarity method and the Maximum Violating Helicity (MVH) Amplitudes that basically consist an alternative way to obtain the ...
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1answer
535 views

Twistor notation in space-time (Part 1)

This is sort of a continuation of this and this previous discussions. In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real ...
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Any practical results yet from 'Twistor Uprising'?

In Nima's lectures on the 'Twistor Uprising' (for example here), he gushes about about new powerful techniques for calculating amplitudes, such as summing Feynman diagrams using 'BCFW recursion.' He ...
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528 views

Twistors in Curved Spacetime

I am looking for good and recent references to constructing twistor space for curved spacetime. This could be a general spacetime, or specific ones (say maximally symmetric spaces different from ...
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2answers
255 views

Kerr Geometry, Separability and Twistors

One of the remarkable properties of the Kerr black hole geometry is that scalar field equations separate and are exactly solvable (reducible to quadrature), even though naively it does not have enough ...
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982 views

twistor-spacetime correspondence

Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice
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3k views

Is there a T-dual of Witten's twistor topological string theory?

In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four ...