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101 0 $aeng
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200 10$aCombinatorial Aspects of Scattering Amplitudes$b[electronic resource] $eAmplituhedra, T-duality, and Cluster Algebras /$fby Matteo Parisi
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023.
215   $a1 online resource (237 pages)
225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061
311 08$aPrint version: Parisi, Matteo Combinatorial Aspects of Scattering Amplitudes Cham : Springer,c2023 9783031410680 
327   $a1. Introduction -- 2. The Amplituhedron -- 3. The Hypersimplex -- 4. T-duality: the Hypersimplex VS the Amplituhedron -- 5. Positroid Triangulations -- 6. The Momentum Amplituhedron -- 7. Cluster Algebras and Amplituhedra -- 8. Conclusions.
330   $aThis book is a significant contribution within and across High Energy Physics and Algebraic Combinatorics. It is at the forefront of the recent paradigm shift according to which physical observables emerge from geometry and combinatorics. It is the first book on the amplituhedron, which encodes the scattering amplitudes of N=4 Yang-Mills theory, a cousin of the theory of strong interactions of quarks and gluons. Amplituhedra are generalizations of polytopes inside the Grassmannian, and they build on the theory of total positivity and oriented matroids. This book unveils many new combinatorial structures of the amplituhedron and introduces a new important related object, the momentum amplituhedron. Moreover, the work pioneers the connection between amplituhedra, cluster algebras and tropical geometry. Combining extensive introductions with proofs and examples, it is a valuable resource for researchers investigating geometrical structures emerging from physics for some time to come.
410  0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061
606   $aElementary particles (Physics)
606   $aQuantum field theory
606   $aAlgebraic geometry
606   $aMathematics
606   $aElementary Particles, Quantum Field Theory
606   $aAlgebraic Geometry
606   $aApplications of Mathematics
615  0$aElementary particles (Physics).
615  0$aQuantum field theory.
615  0$aAlgebraic geometry.
615  0$aMathematics.
615 14$aElementary Particles, Quantum Field Theory.
615 24$aAlgebraic Geometry.
615 24$aApplications of Mathematics.
676   $a530.143
700   $aParisi$b Matteo$01437879
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910760276103321
996   $aCombinatorial Aspects of Scattering Amplitudes$93598710
997   $aUNINA