Combinatorial Aspects of Scattering Amplitudes
Amplituhedra, T-duality, and Cluster Algebras
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Beschreibung
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.
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.
Connects Amplituhedra with the ever-expanding fields of cluster algebras and tropical geometry Addresses both algebraic combinatorists and high energy physicists Combines extensive introductions on both math and physics topics with rigorous proofs and explicatory examples
Autor*in
Matteo Parisi
Themen in »Combinatorial Aspects of Scattering Amplitudes«
Amplituhedron On-shell Methods Landau Singularities Positive Tropical Grassmannian Matroids and Positroids Triangulations T-duality Moment Map Positive Geometry Scattering Amplitudes N=4 super Yang-Mills S-matrix Cluster Algebras Cluster Adjacency Tropical Geometry