03243nam 22005775 450 991076027610332120231109201909.03-031-41069-610.1007/978-3-031-41069-7(MiAaPQ)EBC30878231(Au-PeEL)EBL30878231(DE-He213)978-3-031-41069-7(EXLCZ)992880631650004120231109d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCombinatorial Aspects of Scattering Amplitudes[electronic resource] Amplituhedra, T-duality, and Cluster Algebras /by Matteo Parisi1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Springer,2023.1 online resource (237 pages)Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5061Print version: Parisi, Matteo Combinatorial Aspects of Scattering Amplitudes Cham : Springer,c2023 9783031410680 1. 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.This 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.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5061Elementary particles (Physics)Quantum field theoryAlgebraic geometryMathematicsElementary Particles, Quantum Field TheoryAlgebraic GeometryApplications of MathematicsElementary particles (Physics).Quantum field theory.Algebraic geometry.Mathematics.Elementary Particles, Quantum Field Theory.Algebraic Geometry.Applications of Mathematics.530.143Parisi Matteo1437879MiAaPQMiAaPQMiAaPQBOOK9910760276103321Combinatorial Aspects of Scattering Amplitudes3598710UNINA