Related papers: From multileg loops to trees (by-passing Feynman's…
We exploit a recently found connection between special triple-cut diagrams and tree-level recursive diagrams to derive a general formula capturing the multi-particle factorisation of arbitrary one-loop amplitudes in the ABJM theory. This…
In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the…
We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\phi^3$ theory, from all nestings and chainings of a primitive self-energy…
The action for a relativistic free particle of mass m receives a contribution $-m R(x,y)$ from a path of length R(x,y) connecting the events $x^i$ and $y^i$. Using this action in a path integral, one can obtain the Feynman propagator for a…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(\phi^3)$ amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
A general outlook is presented on the study of multiloop topologies appearing for the first time at four loops. A unified description and representation of this family is provided, the so-called N$^4$MLT universal topology. Based on the…
This is the revised version of Sect. I - IV of the paper https://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. The thing is that in https://doi.org/10.1103/PhysRevD.89.125022 the text was insufficiently clear and, in…
Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
This thesis expands the available techniques at weak coupling by investigating the linear space of Feynman integrals and the role that (super)symmetry plays in reducing the number of integrals necessary to calculate correlators in the…
We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple…
We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of one-loop non-MHV…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
The notion of a unique integrand does not a priori makes sense in field theory: different Feynman diagrams have different loop momenta and there should be no reason to compare them. In string theory, however, a global integrand is natural…
We use the modified propagator for quantum field based on a ``principle of path integral duality" proposed earlier in a paper by Padmanabhan to investigate several results in QED. This procedure modifies the Feynman propagator by the…
By employing the perturbiner method we study the tree- and one-loop-level amplitudes in (anti)self-dual Yang-Mills, focusing on color-kinematics duality and double copy features; they arise naturally even in the fully off-shell case. In…