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Combinatorial aspects of scattering amplitudes = amplituhedra, T-duality, and cluster algebras /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Combinatorial aspects of scattering amplitudes/ by Matteo Parisi.
Reminder of title:	amplituhedra, T-duality, and cluster algebras /
Author:	Parisi, Matteo.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xxiii, 219 p. :illustrations (chiefly color), digital ; : 24 cm.;
Notes:	"Doctoral thesis accepted by University of Oxford, Oxford, UK."
Contained By:	Springer Nature eBook
Subject:	Quantum field theory - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-031-41069-7
ISBN:	9783031410697

Combinatorial aspects of scattering amplitudes = amplituhedra, T-duality, and cluster algebras /
Parisi, Matteo.

Combinatorial aspects of scattering amplitudesamplituhedra, T-duality, and cluster algebras /[electronic resource] :by Matteo Parisi. - Cham :Springer Nature Switzerland :2023. - xxiii, 219 p. :illustrations (chiefly color), digital ;24 cm. - Springer theses,2190-5061. - Springer theses..

"Doctoral thesis accepted by University of Oxford, Oxford, UK."

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.

ISBN: 9783031410697

Standard No.: 10.1007/978-3-031-41069-7doiSubjects--Topical Terms:

796731
Quantum field theory
--Mathematics.

LC Class. No.: QC174.45

Dewey Class. No.: 530.143

Combinatorial aspects of scattering amplitudes = amplituhedra, T-duality, and cluster algebras /
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520 $a 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.
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