Related papers: Master Formulae for $N$-photon tree level amplitud…
We use the recently developed massive spinor-helicity formalism [1] of Arkani- Hamed et al. to propose a new class of recursion relations for tree-level amplitudes in gauge theories. These relations are based on a combined complex…
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…
S-matrix amplitudes for the electron-electron scattering are calculated in order to verify the quantum equivalence of dual models. We used an extended Quantum Electrodynamics with CPT-even Lorentz-violating kinetic and mass terms, which was…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
I consider the singular behaviour of tree-level QCD amplitudes when the momenta of three partons become simultaneously parallel and I discuss the universal factorization formula that controls the singularities of the multiparton matrix…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
We calculate all the four-photon helicity amplitudes at the one-loop level in a massive theory using multiple-cut methods. The amplitudes are derived in scalar QED, QED and $\textrm{QED}^{\caln =1}$ theories. We will see the origin of…
We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because…
We present a new method, exact in $\alpha'$, to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits…
In the first part of this series, we employed the second-order formalism and the ``symbol'' map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open…
Accurate modelling is necessary to support precision experiments investigating strong-field QED phenomena. This modelling is particularly challenging in the transition between the perturbative and nonperturbative regimes, where the…
The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude exp(-I_{classical}/\hbar), where I_{classical} is the Euclidean action of the classical solution…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
In this paper, we study the dynamics of the charged particle interacting with the non-null electromagnetic knot wave background. We analyse the classical system in the Hamilton-Jacobi formalism and find the action, the linear momentum and…
We explicitly compute the Compton amplitude for the scattering of a photon and a (massless) ``electron/positron'' at tree level and one loop, in a four-dimensional fermionic heterotic string model. We comment on the relationship between the…
Categorification of scattering amplitudes for planar Feynman diagrams in scalar field theories with a polynomial potential is reported. Amplitudes for cubic theories are directly written down in terms of projectives of hearts of…
A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…
In this paper, we give the general expressions for a special series of tree amplitudes of the Yang-Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
We explain how nonperturbative effects can be systematically included when constructing an effective field theory. We concentrate in particular on the matching calculation, by which a low energy theory without a heavy particle degree of…