Relevant bibliographies by topics / Amplituhedron

Academic literature on the topic 'Amplituhedron'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Amplituhedron"

1

Bourjaily, Jacob, and Hugh Thomas. "WHAT IS...the amplituhedron?" Notices of the American Mathematical Society 65, no. 02 (February 1, 2018): 167–69. http://dx.doi.org/10.1090/noti1630.

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2

Galashin, Pavel, and Thomas Lam. "Parity duality for the amplituhedron." Compositio Mathematica 156, no. 11 (November 2020): 2207–62. http://dx.doi.org/10.1112/s0010437x20007411.

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The (tree) amplituhedron $\mathcal {A}_{n,k,m}(Z)$ is a certain subset of the Grassmannian introduced by Arkani-Hamed and Trnka in 2013 in order to study scattering amplitudes in $N=4$ supersymmetric Yang–Mills theory. Confirming a conjecture of the first author, we show that when $m$ is even, a collection of affine permutations yields a triangulation of $\mathcal {A}_{n,k,m}(Z)$ for any $Z\in \operatorname {Gr}_{>0}(k+m,n)$ if and only if the collection of their inverses yields a triangulation of $\mathcal {A}_{n,n-m-k,m}(Z)$ for any $Z\in \operatorname {Gr}_{>0}(n-k,n)$. We prove this duality using the twist map of Marsh and Scott. We also show that this map preserves the canonical differential forms associated with the corresponding positroid cells, and hence obtain a parity duality for amplituhedron differential forms.
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Ferro, Livia, Tomasz Łukowski, and Matteo Parisi. "Amplituhedron meets Jeffrey–Kirwan residue." Journal of Physics A: Mathematical and Theoretical 52, no. 4 (December 28, 2018): 045201. http://dx.doi.org/10.1088/1751-8121/aaf3c3.

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Lam, Thomas. "Amplituhedron Cells and Stanley Symmetric Functions." Communications in Mathematical Physics 343, no. 3 (March 19, 2016): 1025–37. http://dx.doi.org/10.1007/s00220-016-2602-2.

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Ferro, Livia, Tomasz Łukowski, Andrea Orta, and Matteo Parisi. "Yangian symmetry for the tree amplituhedron." Journal of Physics A: Mathematical and Theoretical 50, no. 29 (June 29, 2017): 294005. http://dx.doi.org/10.1088/1751-8121/aa7594.

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Łukowski, Tomasz, and Robert Moerman. "Boundaries of the amplituhedron with amplituhedronBoundaries." Computer Physics Communications 259 (February 2021): 107653. http://dx.doi.org/10.1016/j.cpc.2020.107653.

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Ferro, L., T. Lukowski, A. Orta, and M. Parisi. "Tree-level scattering amplitudes from the amplituhedron." Journal of Physics: Conference Series 841 (May 2017): 012037. http://dx.doi.org/10.1088/1742-6596/841/1/012037.

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Karp, Steven N., and Lauren K. Williams. "The $m=1$ Amplituhedron and Cyclic Hyperplane Arrangements." International Mathematics Research Notices 2019, no. 5 (July 24, 2017): 1401–62. http://dx.doi.org/10.1093/imrn/rnx140.

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Łukowski, Tomasz. "On the boundaries of the $m=2$ amplituhedron." Annales de l’Institut Henri Poincaré D 9, no. 3 (December 22, 2022): 525–41. http://dx.doi.org/10.4171/aihpd/124.

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Hodges, Andrew. "Twistors and amplitudes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2047 (August 6, 2015): 20140248. http://dx.doi.org/10.1098/rsta.2014.0248.

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A brief review is given of why twistor geometry has taken a central place in the theory of scattering amplitudes for fundamental particles. The emphasis is on the twistor diagram formalism as originally proposed by Penrose, the development of which has now led to the definition by Arkani-Hamed et al. of the ‘amplituhedron’.
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Dissertations / Theses on the topic "Amplituhedron"

1

Orta, Andrea [Verfasser], and Livia [Akademischer Betreuer] Ferro. "Geometric description of scattering amplitudes : exploring the amplituhedron / Andrea Orta ; Betreuer: Livia Ferro." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1165503778/34.

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SALVATORI, GIULIO. "AMPLITUHEDRA FOR PHI^3 THEORY AT TREE AND LOOP LEVEL." Doctoral thesis, Università degli Studi di Milano, 2019. http://hdl.handle.net/2434/740134.

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In this thesis we explore a novel connection between scattering amplitudes and positive geometries, which are semi-algebraic varieties iteratively defined by the property of possessing a boundary structure which reduces into lower dimensional version of themselves. The relevance of positive geometries in physics was first discovered in the context of scattering amplitudes in N = 4 SYM and led to the definition of the Amplituhedron. An analogue structure was very recently found to tie tree level scattering amplitudes in the bi-adjoint scalar theory to the Stasheff polytope and the moduli space of Riemann surfaces of genus zero. Here we further extend this framework and show how the 1-loop integrand in bi-adjoint theory, or more generally in a planar scalar cubic theory, is connected with moduli spaces of more general Riemann surfaces. We propose hyperbolic geometry to be a natural language to study the positive geometries living in various moduli spaces, then we illustrate convex realizations of polytopes which are combinatorially equivalent to them, but live directly in the kinematical space of amplitudes and integrands. Finally, we show how to exploit these constructions to provide novel and efficient recursive formulae for both tree level amplitudes and 1-loop integrands.
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