Sign Flip Triangulation of the Amplituhedron Ryota Kojima - PowerPoint PPT Presentation

Sign Flip Triangulation of the Amplituhedron Ryota Kojima SOKENDAI, KEK theory centor Based on RK, JHEP 1904 (2019) 085 arxiv:1812.01822 [hep-th] RK, Cameron Langer, Jaroslav Trnka and Minshan Zheng(UC Davis, QMAP), in progress Strings and Fields 2019 at YITP 8/20

Introduction structure of scattering amplitude. in theoretical physics. 2 • Scattering amplitude: Basic objects in QFT. • Recently there are many progress about the understanding of the new • Studying and calculating scattering amplitudes became a new direction • Major motivations: • Efficient calculations of the scattering amplitudes • Use amplitudes as a probe to explore quantum field theory

Introduction (Arkani-Hamed, Bourjaily, Cachazo, Caron-Huot, Trnka 2010) 3 2485 34300 6 220 <latexit sha1_base64="UNc4SGyPxwXJet7OEnzpsxTFaM=">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</latexit> <latexit sha1_base64="UNc4SGyPxwXJet7OEnzpsxTFaM=">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</latexit> <latexit sha1_base64="UNc4SGyPxwXJet7OEnzpsxTFaM=">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</latexit> <latexit sha1_base64="UNc4SGyPxwXJet7OEnzpsxTFaM=">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</latexit> BCFW Feynman diagrams (Britto, Cachazo, Feng, Witten 2005) 3 from BCFW. 20 • Efficient calculations of the scattering amplitudes • Use amplitudes as a probe to explore quantum field theory • Example: BCFW recursion relation • Method for building higher-point amplitudes from lower-point g + g → 4 g, g + g → 5 g, g + g → 6 g • It is possible to calculate all order amplitudes in Planar N=4 SYM

4 (N. Arkani-Hamed, J. Trnka 2013) Introduction “Amplitude = Volume of a geometric object” Example; Planar N=4 SYM The amplituhedron • k-plane in k+m dimensional space • Defined as a generalization of convex polytope. • m=4 ; physical amplituhedron <latexit sha1_base64="rtbfKwWuf3iK8FfI4E6z8Bd1xAI=">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</latexit> <latexit sha1_base64="rtbfKwWuf3iK8FfI4E6z8Bd1xAI=">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</latexit> <latexit sha1_base64="rtbfKwWuf3iK8FfI4E6z8Bd1xAI=">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</latexit> <latexit sha1_base64="rtbfKwWuf3iK8FfI4E6z8Bd1xAI=">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</latexit> • Efficient calculations of the scattering amplitudes • Use amplitudes as a probe to explore quantum field theory • Geometrization of scattering amplitudes A n,m,k ( Z ) Z 1 Z 2 Z n Z 4 A n,k ( Z ) Z 3

Sign Flip Triangulation of the Amplituhedron Ryota Kojima - PowerPoint PPT Presentation

Sign Flip Triangulation of the Amplituhedron Ryota Kojima SOKENDAI, KEK theory centor Based on RK, JHEP 1904 (2019) 085 arxiv:1812.01822 [hep-th] RK, Cameron Langer, Jaroslav Trnka and Minshan Zheng(UC Davis, QMAP), in progress Strings and

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Sign Flip Triangulation of the Amplituhedron Ryota Kojima - PowerPoint PPT Presentation

Sign Flip Triangulation of the Amplituhedron Ryota Kojima SOKENDAI, KEK theory centor Based on RK, JHEP 1904 (2019) 085 arxiv:1812.01822 [hep-th] RK, Cameron Langer, Jaroslav Trnka and Minshan Zheng(UC Davis, QMAP), in progress Strings and

Triangulation of 2-loop MHV Amplituhedron from sign flips Ryota Kojima Sokendai, KEK theory

Scattering amplitudes from the amplituhedron NMHV volume forms Andrea Orta

Triangulation and Convex Hull 8th November 2018 Agenda 1. Triangulation. No book, the slides

CS6100: Topics in Design and Analysis of Algorithms Delaunay Triangulation John Augustine

2D Triangulation Input 2D Boundary Output Triangle Mesh Physical Simulation Yixin Hu, 2 9/5/19

Deep into the Amplituhedron Jaroslav Trnka Center for Quantum Mathematics and Physics (QMAP),

Introduction Voronoi Diagram &amp; Delaunay Triangulation P = { p 1 , p 2 , , p n } a set of n

Atomic page flip and mode setting Hardware structure and abstraction Atomic page flip The

Bob Martinez &amp; Eddie Tchertchian Pierce College FTLA 2018 Do A Flip! How to set up and run

Four point scattering from Amplituhedron Jaroslav Trnka Caltech Nima Arkani-Hamed, JT,

Triangulation applied to the identification of evaluation findings Experiences with systematic

On a Linear Program for Minimum Weight Triangulation Arman Yousefi and Neal Young University of

T flip flop (toggle) TODAY: from flip flops to RAM lecture 6 Sequential circuits 2 Assume

Flip-Flops Assume the an edge-triggered flip-flop FF implements a Boolean function f with

Flip Distances between Graph Orientations Jean Cardinal Joint work with Oswin Aichholzer, Tony

Flip Video: A Tool for Itinerant Educators April, 2010 Patti Glumack Deb Williamson Flip Video

for a sign! But none will be given it except the sign of the prophet Jonah. 40 40 For as Jonah was

Polygon Triangulation Computational Geometry The Art Gallery Problem Guarding and

Real-rootedness results for triangulation operations inspired by the Tchebyshev polynomials G

Efficiently navigating a random Delaunay triangulation Nicolas Broutin, Olivier Devillers, Ross

Truncated Stanley symmetric functions and amplituhedron cells Thomas Lam June 2014 Reduced

Triangulation Its a matter of perspective Paul Howarth CEO Pansensic About

Digital Design Discussion: Flip-Flops D-Latch Design Latch vs. Flip-Flop Timing D-latch Design

Triangulation complexity of fibred 3-manifolds Jessica Purcell, joint with M. Lackenby CUNY 2020

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