Related papers: Note on recursion relations for the $\mathcal{Q}$-…
Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
In this talk we discuss the color decomposition of tree-level and one-loop QCD amplitudes with arbitrary numbers of quarks and gluons. We present a method for the decomposition of partial amplitudes into primitive amplitudes, which is based…
We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…
In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
We develop a systematic procedure for computing maximal unitarity cuts of multiloop Feynman integrals in arbitrary dimension. Our approach is based on the Baikov representation in which the structure of the cuts is particularly simple. We…
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop $N$-point corrections are needed. We study here the tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive solution by…
We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to…
Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one…
We present an analytic technique for evaluating single cuts for one-loop integrands, where exactly one propagator is taken to be on shell. Our method extends the double-cut integration formalism of one-loop amplitudes to the single-cut…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
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…
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…
Recently it has been shown that in gauge theories amplitudes to any perturbation order can be obtained by glueing together simple three-point on-shell amplitudes. These three-point amplitudes in turn are fixed by locality and Lorentz…
In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…
We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master…