Skip to main content

Questions tagged [twistor]

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
38 views

Building vector Noether current from twistor using Dirac formalism

There was a problem formulated during our lectures to build a Killing vector $$ \nabla_{(\mu} k_{\nu)} = 0 $$ from equation $$ {\nabla_{(C}}^{\dot{D}} \varkappa_{A)} = 0. $$ For me it seems that $$ k_\...
Iowo's user avatar
  • 11
1 vote
1 answer
56 views

"Fourier Transformation" of angle spinors to twistor variables

This relates to the derivation of equation (5.15) if Elvang and Huang's textbook. The idea is to transform the spinor helicity variables we are using, $(|i\rangle_{\dot{a}},[j|^a)$ to go into twistor ...
MathZilla's user avatar
  • 704
0 votes
0 answers
16 views

How do reality conditions on complexified Minkowski space induce conjugation on Spinor space

So I am following this script here: https://arxiv.org/abs/1712.02196 I am already stuck at chapter 1.3: I understand for the three cases Lorentzian, Euclidean and Split case that the coordinates need ...
Confuse-ray30's user avatar
2 votes
0 answers
66 views

What is the difference between a twistor and bispinor?

Reading the book on General Relativity written by R.M. Wald I (tags according to Wald's book) encountered the concept of a twistor $$ Z = (\omega^A, \pi_{A'}) \tag{14.1.9} $$ which looks very much as ...
Frederic Thomas's user avatar
1 vote
0 answers
38 views

BMS transformation of Twistors at Infinity

As the title suggest, is it known how a twistor variable will transform under the action of BMS transformation? Consider the 2-twistor construction on Null Infinity. One suggestion that I got online ...
paul230_x's user avatar
  • 1,752
3 votes
0 answers
58 views

Twistor equation and Killing equation

Yesterday was the birthday of Roger Penrose. And reading again about twistors I realized that twistor equation is strikingly similar to a Killing equation. My question is, are they "equivalent&...
riemannium's user avatar
  • 6,611
0 votes
0 answers
91 views

How does the Pauli Exclusion Principle work in Twistor theory?

Twistor theory is described sometimes as a 'natural' way to represent spinor fields. In QED, we have the Grassmann valued spinor field $\Psi^\alpha(x)$, which naturally leads to the exclusion ...
user avatar
1 vote
0 answers
72 views

Two-twistors formulation vs twistors formulation

I have seen in some research work that the classic formulation using twistors (introduced by Penrose) is replaced with a formulation that considers two-twistors. For example the linking article says ...
user avatar
4 votes
1 answer
276 views

Path integral formulation in Twistor theory?

Sir R. Penrose in his article (https://doi.org/10.1007/BF00668831) has shown that there are close similarities in various aspects of twistor theory and quantum mechanics. In twistor theory, one can ...
paul230_x's user avatar
  • 1,752
5 votes
1 answer
230 views

Non-locality and Twistor functions

Is there a nice intuitive way to visualize the concept of non-locality associated to twistor functions? And how is it related to the type of non-locality we encounter in Quantum Mechanics?
paul230_x's user avatar
  • 1,752
4 votes
1 answer
278 views

Spin $1/2$ motivation for twistor theory in general relativity?

I was watching this Youtube video (I have linked it at the relevant timestamp) and to paraphrase Dr. Woit' s motivation for twistor theory: Within the standard way of thinking about general ...
More Anonymous's user avatar
0 votes
2 answers
137 views

Twistor and Calabi-Yau spaces

The twistor space of Penrose's twistor theory is a projective space of three complex dimensions. This can be understood as six orthogonal dimensions, three with real metric and three with imaginary ...
Guy Inchbald's user avatar
  • 7,438
2 votes
1 answer
77 views

Homogeneous (projective) coordinates and spinors

When a complex number is considered as the stereographic projection from a sphere to the Argand plane, and then is represented by two “homogeneous coordinates” (in order to allow for a “point at ...
gabe's user avatar
  • 41
1 vote
1 answer
72 views

Need examples of spinor pairs in twistor theory

I’m stuck on a basic introductory point regarding twistors. I understand the mapping of 4-vectors to hermitian matrices, and the incidence relation defined by pairs of spinors. And I understand that a ...
gabe's user avatar
  • 41
2 votes
0 answers
209 views

Book recommendations about differential geometry for the study of twistors

I'm in my first year as a PhD student and I'm trying to learn about twistors. I found the question about the book recommendations for twistor theory, but it quickly became clear that my knowledge of ...
4 votes
2 answers
234 views

Could graviton exist in a single polarisation?

Penrose's twistor theory can only construct a left-handed graviton. This is seen as a problem. But... is there anything wrong with gravitons existing in only one polarisation? How would gravity differ ...
user avatar
2 votes
1 answer
171 views

Why are twistors commuting?

In his book, Srednicki introduces the notion of twistor in chapter 50. It is described as a simply commuting spinor, as opposed to anti-commuting. How do we know that this object is simply commuting? ...
Whelp's user avatar
  • 4,036
1 vote
0 answers
23 views

Hypertwistors and matrices

Just as twistors can be understood as certain objects invariant under SU(2,2), and SU(2,2/N) are the corresponding to supertwistors in supermatrices: What is the fundamental matrix invariance ...
riemannium's user avatar
  • 6,611
2 votes
0 answers
78 views

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 ...
Brad's user avatar
  • 65
3 votes
1 answer
950 views

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 ...
sztorwi's user avatar
  • 91
1 vote
0 answers
86 views

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 $\mathbb{C}\mathbb{P}^3$. ...
Brad's user avatar
  • 65
6 votes
2 answers
1k views

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 ${\rm SO}^+(3,1)$. ...
SRS's user avatar
  • 26.8k
2 votes
0 answers
62 views

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 ...
riemannium's user avatar
  • 6,611
1 vote
0 answers
161 views

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 ...
Rythian's user avatar
  • 11
-1 votes
1 answer
203 views

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 ...
XXDD's user avatar
  • 1,548
2 votes
0 answers
198 views

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 ...
Lawrence B. Crowell's user avatar
2 votes
0 answers
189 views

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-...
giulio bullsaver's user avatar
3 votes
1 answer
264 views

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 ...
raul's user avatar
  • 428
2 votes
0 answers
262 views

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, ...
raul's user avatar
  • 428
4 votes
0 answers
237 views

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 ...
XXDD's user avatar
  • 1,548
3 votes
0 answers
161 views

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 ...
XXDD's user avatar
  • 1,548
3 votes
1 answer
418 views

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 ...
user46523's user avatar
4 votes
0 answers
177 views

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 ...
user avatar
8 votes
1 answer
385 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 ...
Prathyush's user avatar
  • 2,032
2 votes
0 answers
135 views

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 $\phi^{A\dots B}$ ...
Edward Hughes's user avatar
4 votes
2 answers
223 views

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 ...
Edward Hughes's user avatar
9 votes
1 answer
771 views

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 ...
Dilaton's user avatar
  • 9,581
5 votes
1 answer
981 views

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 ...
Dilaton's user avatar
  • 9,581
2 votes
0 answers
446 views

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 ...
Aftnix's user avatar
  • 929
30 votes
3 answers
9k views

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. ...
10 votes
3 answers
1k views

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 ...
user56771's user avatar
  • 873
3 votes
1 answer
827 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 ...
user6818's user avatar
  • 4,619
9 votes
1 answer
469 views

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 ...
user1247's user avatar
  • 7,398
22 votes
3 answers
840 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 ...
user avatar
21 votes
2 answers
391 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 ...
user avatar
7 votes
3 answers
1k views

twistor-spacetime correspondence

Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice
lurscher's user avatar
  • 14.5k
32 votes
2 answers
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 ...
Luboš Motl's user avatar