Related papers: QED amplitudes: recurrence relations to all orders
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present…
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine…
We derive a recursion relation for loop-level scattering amplitudes of Lagrangian field theories that generalises the tree-level Berends-Giele recursion relation in Yang-Mills theory. The origin of this recursion relation is the homological…
We show how to apply the BCFW recursion relation to Feynman loop integrals with the help of the Feynman-tree theorem. We deconstruct in this way all Feynman diagrams in terms of on-shell subamplitudes. Every cut originating from the…
Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint $\phi^3$ theory. The recursion relies on properties of…
We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
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…
The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
Using the method of on-shell recursion relations we compute tree level amplitudes including D-dimensional scalars and fermions. These tree level amplitudes are needed for calculations of one-loop amplitudes in QCD involving external quarks…
Using light cone string field theory we derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory. These results extend to strings in a plane wave…
The purpose of this review is to bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes. We build up the subject from basic quantum field theory,…
The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be…
We show that on-shell recursion relations hold for tree amplitudes in generic two derivative theories of multiple particle species and diverse spins. For example, in a gauge theory coupled to scalars and fermions, any amplitude with at…
We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each…
QCD amplitudes with many external fields have been studied for a long time. At tree-level, the amplitudes can be obtained effectively by the BCFW recursion relations. In this article, we extend the Britto-Cachazo-Feng-Witten (BCFW)…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…