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We present novel techniques for the computation of three-loop four-parton scattering amplitudes in full color, non-planar gauge theories. We elaborate on how the analytic results for these amplitudes can be used to confirm the conjectured…
We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…
We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules,…
We postulate that the Fermi function should be derived from the amplitude, not from the solution of the Dirac equation, in the quantum field theory. Then, we obtain the following results. 1, We give the amplitude and the width of the…
Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to…
We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. By promoting the group theory Fourier modes into creation and annihilation…
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of…
Counting the contribution rate of a world-line formula to Feynman diagrams in $\phi^3$ theory, we explain the idea how to determine precise combinatorics of Bern-Kosower-like amplitudes derived from a bosonic string theory for $N$-point…
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is…
Feynman amplitudes of light-cone gauge superstring field theory are ill-defined because of various divergences. In a previous paper, one of the authors showed that taking the worldsheet theory to be the one in a linear dilaton background…
This thesis discusses how the pure spinor formalism can be used to efficiently compute superstring scattering amplitudes. We emphasize the pure spinor superspace form of the kinematic factors, where the simplifying features of this language…
We compute the three-loop scattering amplitude of four gravitons in ${\mathcal N}=8$ supergravity. Our results are analytic formulae for a Laurent expansion of the amplitude in the regulator of dimensional regularisation. The coefficients…
We present technical details of the evaluation of the elastic pi-pi scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of…
We present an overview of the analysis of the multiloop topologies that appear for the first time at four loops and the assembly of them in a general expression, the N$^4$MLT universal topology. Based on the fact that the Loop-Tree Duality…
We derive a representation for the pion nucleon scattering amplitude that is valid to the fourth order of the chiral expansion. To obtain the correct analytic structure of the singularities in the low energy region, we have performed the…
We calculate the spin-averaged amplitude for doubly virtual forward Compton scattering off nucleons in the framework of manifestly Lorentz invariant baryon chiral perturbation theory at complete one-loop order $O(p^4)$. The calculations are…
We discuss a remarkable new approach initiated by Cachazo, Svrcek and Witten for calculating gauge theory amplitudes. The formalism amounts to an effective scalar perturbation theory which in many cases offers a much simpler alternative to…
We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4 super-Yang-Mills theory employing an algebraic representation of amplitudes. In this language, we reproduce the deformed massless box integral describing the…
The inverse amplitude method is analysed to two-loop order in the chiral expansion in the case of $\pi\pi$ scattering and the pion form factors. The analysis is mainly restricted to the elastic approximation but the possible extension to…
We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the…