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View article: Coaction and double-copy properties of configuration-space integrals at genus zero
Coaction and double-copy properties of configuration-space integrals at genus zero Open
We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose…
View article: Generalized Cuts of Feynman Integrals in Parameter Space
Generalized Cuts of Feynman Integrals in Parameter Space Open
We propose a construction of generalized cuts of Feynman integrals as an operation on the domain of the Feynman parametric integral. A set of on-shell conditions removes the corresponding boundary components of the integration domain, in f…
View article: Generalized Cuts of Feynman Integrals in Parameter Space
Generalized Cuts of Feynman Integrals in Parameter Space Open
We propose a construction of generalized cuts of Feynman integrals as an operation on the domain of the Feynman parametric integral. A set of on-shell conditions removes the corresponding boundary components of the integration domain, in f…
View article: The diagrammatic coaction
The diagrammatic coaction Open
The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respective…
View article: The SAGEX review on scattering amplitudes Chapter 3: Mathematical structures in Feynman integrals
The SAGEX review on scattering amplitudes Chapter 3: Mathematical structures in Feynman integrals Open
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for …
View article: The SAGEX review on scattering amplitudes*
The SAGEX review on scattering amplitudes* Open
This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of…
View article: The Diagrammatic Coaction
The Diagrammatic Coaction Open
The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respective…
View article: Proving the dimension-shift conjecture
Proving the dimension-shift conjecture Open
We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that describes a simple dimension shifting relationship between the one-loop structure of \mathcal{N}=4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills th…
View article: The SAGEX Review on Scattering Amplitudes
The SAGEX Review on Scattering Amplitudes Open
This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of…
View article: The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals Open
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for …
View article: Graviton particle statistics and coherent states from classical scattering amplitudes
Graviton particle statistics and coherent states from classical scattering amplitudes Open
A bstract In the two-body scattering problem in general relativity, we study the final graviton particle distribution using a perturbative approach. We compute the mean, the variance and the factorial moments of the distribution from the e…
View article: Proving the dimension-shift conjecture
Proving the dimension-shift conjecture Open
We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that describes a simple dimension shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. The…
View article: Diagrammatic Coaction of Two-Loop Feynman Integrals
Diagrammatic Coaction of Two-Loop Feynman Integrals Open
When evaluating Feynman integrals as Laurent series in the dimensional regulator epsilon one encounters families of iterated integrals, the simplest of which are the multiple polylogarithms. These functions are known to possess a structure…
View article: Generalized hypergeometric functions and intersection theory for Feynman integrals
Generalized hypergeometric functions and intersection theory for Feynman integrals Open
Feynman integrals that have been evaluated in dimensional regularization can\nbe written in terms of generalized hypergeometric functions. It is well known\nthat properties of these functions are revealed in the framework of\nintersection …
View article: Diagrammatic Coaction of Two-Loop Feynman Integrals
Diagrammatic Coaction of Two-Loop Feynman Integrals Open
It is known that one-loop Feynman integrals possess an algebraic structure encoding some of their analytic properties called the coaction, which can be written in terms of Feynman integrals and their cuts. This diagrammatic coaction, and t…
View article: Generalized hypergeometric functions and intersection theory for Feynman integrals
Generalized hypergeometric functions and intersection theory for Feynman integrals Open
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection the…
View article: Coaction for Feynman integrals and diagrams
Coaction for Feynman integrals and diagrams Open
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and graph…
View article: Coaction for Feynman integrals and diagrams
Coaction for Feynman integrals and diagrams Open
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and graph…
View article: The diagrammatic coaction and the algebraic structure of cut Feynman integrals
The diagrammatic coaction and the algebraic structure of cut Feynman integrals Open
We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coa…
View article: Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction
Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction Open
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. I…