Related papers: Loops and trees
This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$\phi^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the…
The understanding of the physical laws determining the infrared behaviour of amplitudes is a longstanding and topical problem. In this paper, we show that energy conservation alone implies strong constraints on the threshold singularity…
We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized $D$-dimensional unitarity. It allows automated computations of both cut-constructible {\it and} rational parts of one-loop scattering…
We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. This work begins with the observation that three different communities, largely independently, found substantially…
In a way analogous to type IIB supergravity, we give a covariant action for the fermion field supplemented with a constraint which should be imposed on equations of motion, in Berkovits' open superstring field theory. From this action we…
In this paper, we investigate the $2$-split behavior of tree-level amplitudes of bi-adjoint scalar (BAS), Yang-Mills (YM), non-linear sigma model (NLSM), and general relativity (GR) theories under certain kinematic conditions. Our approach…
We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating…
We describe the origins of recurrence relations between field theory amplitudes in terms of the construction of Feynman diagrams. In application we derive recurrence relations for the amplitudes of QED which hold to all loop orders and for…
Solutions of the classical $\phi^4$-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree…
We study loop corrections to scattering amplitudes in the world-volume theory of a probe D3-brane, which is described by the supersymmetric Dirac-Born-Infeld theory. We show that the D3-brane loop superamplitudes can be obtained from the…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
We study the on-shell scattering amplitudes in quantum gravity for high-energy collisions in the eikonal approximation. We first evaluate the $n$-loop 2-particle scattering amplitude in the high energy and low momentum transfer limit. We do…
The idea of adding particles to construct amplitudes has been utilized in various ways in exploring the structure of scattering amplitudes. This idea is often called Inverse Soft Limit, namely it is the reverse mechanism of taking particles…
We discuss the threshold tree amplitudes in diverse nonintegrable quantum field theories in the framework of integrability. The amplitudes are related to some Baker functions defined on the auxiliary spectral curves and the nullification…
We study double copy relations for loop integrands in gauge theories and gravity based on their constructions from single cuts, which are in turn obtained from forward limits of lower-loop cases. While such a construction from forward…
Using the spectral properties of orthogonal polynomials, we introduce a finite version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are finite.…
We present on the use of on-shell recursion relations. These can be used not only for calculating tree amplitudes, including those with masses, but also to compute analytically the missing rational terms of one-loop QCD amplitudes. Combined…
Using the {\em cutting and sewing} procedure we show how to get Feynman diagrams, up to two-loop order, of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a…
In this talk, we review the basis of the loop-tree duality theorem, which allows to rewrite loop scattering amplitudes in terms of tree-level like objects. Since the loop measure is converted into a phase-space one, both virtual and real…
Within the non-perturbative 1/N expansion, we discuss numerical methods for calculating multi-loop Feynman graph needed to derive physical scattering amplitudes. We apply higher order 1/N methods to the scalar sector of the standard model,…