Related papers: Scattering Equations and Feynman Diagrams
The Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integral's dependence within group orbits.…
In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple…
We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve…
We introduce Feynman-like rules to compute quivers for two loops and higher for the coloured planar $\phi^3$ theory for winding number zero. We demonstrate this for a few cases. Then we extend this further to the case of $\phi^n$ theories,…
In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories. Recently, an interesting generalization of the bi-adjoint…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
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…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We study a two loop diagram of propagator type with general parameters through the Symmetries of Feynman Integrals (SFI) method. We present the SFI group and equation system, the group invariant in parameter space and a general…
We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these…
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees…
We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural…
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…
The symmetry factor of Feynman diagrams for real and complex scalar fields is presented. Being analysis of Wick expansion for Green functions, the mentioned factor is derived in a general form. The symmetry factor can be separated into two…
In this note, we introduce and study a new class of "half integrands" in Cachazo-He-Yuan (CHY) formula, which naturally generalize the so-called Parke-Taylor factors; these are dubbed Cayley functions as each of them corresponds to a…
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops.…
In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral $\mathrm{sl}(2,\mathbb{C})$ nature of spacetime. While our previous work…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…