Related papers: Alphabet of one-loop Feynman integrals
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and…
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…
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 provide a systematic derivation of cluster alphabets of finite types. The construction is based on a geometric realization of the generalized worldsheets by gluing and folding a pair of polygons. The cross ratios of the worldsheet z…
By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore…
Decay amplitude of $H \to \gamma Z$ process via one $W$ loop in the unitary gauge is presented. The divergent integrals including those of high divergence orders typical of unitary gauge are arranged to cancel to get the electromagnetic…
We present an analytic calculation of three-loop four-point Feynman integrals with two off-shell legs of equal mass. We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical…
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…
We present a new algorithm for the reduction of one-loop \emph{tensor} Feynman integrals with $n\leq 4$ external legs to \emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l \geq 0$ and…
We study a two-loop four-point function with one internal mass. This Feynman integral is one of the simplest Feynman integrals depending on two elliptic curves. We transform the associated differential equation into an $\varepsilon$-form.…
We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then,…
Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle,…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits), together with two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a…
We investigate Feynman diagrams which are calculable in terms of generalized one-loop functions, and explore how the presence or absence of transcendentals in their counterterms reflects the entanglement of link diagram constructed from…
Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the UV-divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…