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＜E-Book＞
Combinatorial Aspects of Scattering Amplitudes : Amplituhedra, T-duality, and Cluster Algebras / by Matteo Parisi
(Springer Theses, Recognizing Outstanding Ph.D. Research. ISSN:21905061)

Edition	1st ed. 2023.
Publisher	(Cham : Springer Nature Switzerland : Imprint: Springer)
Year	2023
Language	English
Size	XXIII, 219 p. 53 illus., 40 illus. in color : online resource
Authors	*Parisi, Matteo author SpringerLink (Online service)
Subjects	LCSH:Elementary particles (Physics) LCSH:Quantum field theory LCSH:Algebraic geometry LCSH:Mathematics FREE:Elementary Particles, Quantum Field Theory FREE:Algebraic Geometry FREE:Applications of Mathematics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-031-41069-7

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