Global InformationAmplituhedron information
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In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory, also equivalent to the perturbative topological B model string theory in twistor space, an amplituhedron is defined as a mathematical space known as the positive Grassmannian.[1][2]
Amplituhedron theory challenges the notion that spacetime locality and unitarity are necessary components of a model of particle interactions. Instead, they are treated as properties that emerge from an underlying phenomenon.[3][4]
The connection between the amplituhedron and scattering amplitudes is a conjecture that has passed many non-trivial checks, including an understanding of how locality and unitarity arise as consequences of positivity.[1] Research has been led by Nima Arkani-Hamed. Edward Witten described the work as "very unexpected" and said that "it is difficult to guess what will happen or what the lessons will turn out to be".[5]
- ^ a b Arkani-Hamed, Nima; Trnka, Jaroslav (2014). "The Amplituhedron". Journal of High Energy Physics. 2014 (10): 30. arXiv:1312.2007. Bibcode:2014JHEP...10..030A. doi:10.1007/JHEP10(2014)030. S2CID 7717260.
- ^ Witten, Edward (2004). "Perturbative Gauge Theory As A String Theory In Twistor Space". Communications in Mathematical Physics. 1. 252 (1): 189–258. arXiv:hep-th/0312171. Bibcode:2004CMaPh.252..189W. doi:10.1007/s00220-004-1187-3. S2CID 14300396.
- ^ Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy; Goncharov, Alexander B.; Postnikov, Alexander; Trnka, Jaroslav (2012). "Scattering Amplitudes and the Positive Grassmannian". arXiv:1212.5605 [hep-th].
- ^ Ryan O'Hanlon (September 19, 2013). "How to Feel About Space and Time Maybe Not Existing". Pacific Standard.
- ^ Natalie Wolchover (September 17, 2013). "A Jewel at the Heart of Quantum Physics". Quanta Magazine.