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pro vyhledávání: '"Parisi, Matteo"'
The amplituhedron $A_{n,k,m}$ is a geometric object introduced in the context of scattering amplitudes in $N=4$ super Yang Mills. It generalizes the positive Grassmannian (when $n=k+m$), cyclic polytopes (when $k=1$), and the bounded complex of the c
Externí odkaz:
http://arxiv.org/abs/2404.03026
Autor:
Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Tessler, Ran, Sherman-Bennett, Melissa, Williams, Lauren
The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in $\mathcal{N}=4$ super Yang Mills theory. It generalizes \emph{cyclic polytopes} and the \emph{positive Grassmannian}, and has a
Externí odkaz:
http://arxiv.org/abs/2402.15568
Autor:
Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Tessler, Ran, Sherman-Bennett, Melissa, Williams, Lauren
The amplituhedron $A_{n,k,m}(Z)$ is the image of the positive Grassmannian $Gr_{k,n}^{\geq 0}$ under the map ${Z}: Gr_{k,n}^{\geq 0} \to Gr_{k,k+m}$ induced by a positive linear map $Z:\mathbb{R}^n \to \mathbb{R}^{k+m}$. Motivated by a question of Ho
Externí odkaz:
http://arxiv.org/abs/2310.17727
The hypersimplex $\Delta_{k+1,n}$ is the image of the positive Grassmannian $Gr^{\geq 0}_{k+1,n}$ under the moment map. It is a polytope of dimension $n-1$ in $\mathbb{R}^n$. Meanwhile, the amplituhedron $\mathcal{A}_{n,k,2}(Z)$ is the projection of
Externí odkaz:
http://arxiv.org/abs/2104.08254
Publikováno v:
Commun. Math. Phys. 387, 927-972 (2021)
Any totally positive $(k+m)\times n$ matrix induces a map $\pi_+$ from the positive Grassmannian ${\rm Gr}_+(k,n)$ to the Grassmannian ${\rm Gr}(k,k+m)$, whose image is the amplituhedron $\mathcal{A}_{n,k,m}$ and is endowed with a top-degree form cal
Externí odkaz:
http://arxiv.org/abs/2010.07254
Autor:
Gürdoğan, Ömer, Parisi, Matteo
We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory. In particular we conjecture that, given a maximal cut of a loop amplitude, Landau singularities and p
Externí odkaz:
http://arxiv.org/abs/2005.07154
Autor:
Benincasa, Paolo, Parisi, Matteo
Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables, are charact
Externí odkaz:
http://arxiv.org/abs/2005.03612
The study of the moment map from the Grassmannian to the hypersimplex, and the relation between torus orbits and matroid polytopes, dates back to the foundational 1987 work of Gelfand-Goresky-MacPherson-Serganova. On the other hand, the amplituhedron
Externí odkaz:
http://arxiv.org/abs/2002.06164
We classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit formula for all invaria
Externí odkaz:
http://arxiv.org/abs/1908.07618