scholarly journals Ambidextrous light transforms for celestial amplitudes

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Atul Sharma
Keyword(s):  
Fourier Transforms ◽  
Twistor Space ◽  
Tree Level ◽  
Positive Energy ◽  
Helicity State ◽  
Negative Helicity ◽  
Energy Constraints

Abstract Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z,$$ \overline{z} $$ z ¯ . We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten’s half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate z and every negative helicity state in $$ \overline{z} $$ z ¯ . With examples, we show that this “ambidextrous” prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for n-point Nk−2MHV amplitudes take the form of Euler-type integrals over regions in Gr(k, n) cut out by positive energy constraints.

scholarly journals Evaluating EYM amplitudes in four dimensions by refined graphic expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hongxiang Tian ◽  
Enze Gong ◽  
Chongsi Xie ◽  
Yi-Jian Du
Keyword(s):  
Tree Level ◽  
Tree Amplitude ◽  
Four Dimensions ◽  
Yang Mills ◽  
Negative Helicity ◽  
Spanning Forests ◽  
Single Trace

Abstract The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

YANG-MILLS AMPLITUDES FROM STRING THEORY IN TWISTOR SPACE

2005 ◽  
Vol 20 (15) ◽  
pp. 3416-3419 ◽  
Author(s):  
MARCUS SPRADLIN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Twistor Space ◽  
Mathematical Structure ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Algebraic Equations ◽  
Yang Mills

Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel way of calculating these amplitudes, motivated by a conjectured relation to twistor space, in which the problem of summing Feynman diagrams is replaced by the problem of solving a certain set of algebraic equations.

scholarly journals A new Wilson line-based action for gluodynamics

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hiren Kakkad ◽  
Piotr Kotko ◽  
Anna Stasto
Keyword(s):  
Canonical Transformation ◽  
Light Cone ◽  
Wilson Line ◽  
Functional Derivative ◽  
Tree Level ◽  
Classical Action ◽  
Light Cone Gauge ◽  
Standard Methods ◽  
Yang Mills ◽  
Negative Helicity

Abstract We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $$ \overline{\mathrm{MHV}} $$ MHV ¯ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any n-leg vertex has 2 ≤ m ≤ n − 2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.

scholarly journals $$ \mathcal{N} $$ = 7 On-shell diagrams and supergravity amplitudes in momentum twistor space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Connor Armstrong ◽  
Joseph A. Farrow ◽  
Arthur E. Lipstein
Keyword(s):  
Scattering Amplitudes ◽  
Twistor Space ◽  
Tree Level ◽  
Yang Mills

Abstract We derive an on-shell diagram recursion for tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 7 supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $$ \mathcal{N} $$ N = 7 R-invariants analogous to those of $$ \mathcal{N} $$ N = 4 super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.

scholarly journals All tree-level MHV form factors in N $$ \mathcal{N} $$ = 4 SYM from twistor space

2016 ◽  
Vol 2016 (6) ◽  
Author(s):  
Laura Koster ◽  
Vladimir Mitev ◽  
Matthias Staudacher ◽  
Matthias Wilhelm
Keyword(s):  
Twistor Space ◽  
Form Factors ◽  
Tree Level

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

Observations of Frozen-Hydrated Microtubules

1990 ◽  
Vol 48 (1) ◽  
pp. 504-505
Author(s):  
D. Chrétien ◽  
D. Job ◽  
R.H. Wade
Keyword(s):  
Fourier Transforms ◽  
Structural Complexity ◽  
Image Contrast ◽  
Phase Behaviour ◽  
Experimental Conditions ◽  
Thin Sections ◽  
Surface Lattice ◽  
Cilia And Flagella ◽  
Outstanding Question

Microtubules are filamentary structures found in the cytoplasm of eukaryotic cells, where, together with actin and intermediate filaments, they form the components of the cytoskeleton. They have many functions and show various levels of structural complexity as witnessed by the singlet, doublet and triplet structures involved in the architecture of centrioles, basal bodies, cilia and flagella. The accepted microtubule model consists of a 25 nm diameter hollow tube with a wall made up of 13 paraxial protofilaments (pf). Each pf is a string of aligned tubulin dimers. Some results have suggested that the pfs follow a superhelix. To understand how microtubules function in the cell an accurate model of the surface lattice is one of the requirements. For example the 9x2 architecture of the axoneme will depend on the organisation of its component microtubules. We should also note that microtubules with different numbers of pfs have been observed in thin sections of cellular and of in-vitro material. An outstanding question is how does the surface lattice adjust to these different pf numbers?We have been using cryo-electron microscopy of frozen-hydrated samples to study in-vitro assembled microtubules. The experimental conditions are described in detail in this reference. The results obtained in conjunction with thin sections of similar specimens and with axoneme outer doublet fragments have already allowed us to characterise the image contrast of 13, 14 and 15 pf microtubules on the basis of the measured image widths, of the the image contrast symmetry and of the amplitude and phase behaviour along the equator in the computed Fourier transforms. The contrast variations along individual microtubule images can be interpreted in terms of the geometry of the microtubule surface lattice. We can extend these results and make some reasonable predictions about the probable surface lattices in the case of other pf numbers, see Table 1. Figure 1 shows observed images with which these predictions can be compared.

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