Results 41 to 50 of about 2,492,523 (198)

Weights and recursion relations for ϕ p tree amplitudes from the positive geometry

Journal of High Energy Physics, 2020
Recently, the accordiohedron in kinematic space was proposed as the positive geometry for planar tree-level scattering amplitudes in the ϕ p theory [1]. The scattering amplitudes are given as a weighted sum over canonical forms of some accordiohedra with
Ryota Kojima
doaj   +1 more source

Notes on biadjoint amplitudes, Trop G(3, 7) and X(3, 7) scattering equations

Journal of High Energy Physics, 2020
In these notes we use the recently found relation between facets of tropical Grassmannians and generalizations of Feynman diagrams to compute all “biadjoint amplitudes” for n = 7 and k = 3.
Freddy Cachazo, Jairo M. Rojas
doaj   +1 more source

Kinematic singularities of Feynman integrals and principal A-determinants

Journal of High Energy Physics, 2022
We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A $$ \mathcal{A} $$ -hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ).
René Pascal Klausen
doaj   +1 more source

Differential Geometry Revisited by Biquaternion Clifford Algebra [PDF]

, 2015
In the last century, differential geometry has been expressed within various calculi: vectors, tensors, spinors, exterior differential forms and recently Clifford algebras. Clifford algebras yield an excellent representation of the rotation group and of the Lorentz group which are the cornerstones of the theory of moving frames.
Girard, Patrick, Clarysse, Patrick, Pujol, Romaric, Wang, Liang, Delachartre, Philippe   +4 more
openaire   +4 more sources

On positive geometries of quartic interactions: Stokes polytopes, lower forms on associahedra and world-sheet forms

Journal of High Energy Physics, 2020
In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal.
P.B. Aneesh, Pinaki Banerjee, Mrunmay Jagadale, Renjan Rajan John, Alok Laddha, Sujoy Mahato   +5 more
doaj   +1 more source

Differential-algebraic systems are generically controllable and stabilizable [PDF]

, 2021
We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in ...
Kirchhoff, Jonas, Ilchmann, Achim, Achim Ilchmann, Jonas Kirchhoff   +3 more
core   +1 more source

Rationality in Differential Algebraic Geometry [PDF]

, 2015
Abel Symposium ...
openaire   +2 more sources

The CEGM NLSM

Journal of High Energy Physics
Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes.
Nick Early
doaj   +1 more source

Extreme 5-dimensional black holes with SU(2)-symmetric horizons

Journal of High Energy Physics
We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit SU(2) symmetry must be that of a Berger sphere.
Eric Bahuaud, Sharmila Gunasekaran, Hari K Kunduri, Eric Woolgar   +3 more
doaj   +1 more source

Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2016
Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
openaire   +6 more sources