Related papers: Recursive computation of Feynman periods
We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman…
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
Numerical approaches to computations typically reconstruct the numerators of Feynman diagrams in four dimensions. In doing so, certain rational terms arising from the (D-4)-dimensional part of the numerator multiplying ultraviolet (UV)…
A precise calculation of the lepton anomalous magnetic moments (AMM) requires an evaluation of the quantum electrodynamics (QED) Feynman diagrams up to five independent loops. The complicated structure of ultraviolet (UV), infrared (IR) and…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial…
We explain how to tropicalize scalar quantum field theory and show that tropicalized massive scalar quantum field theory is exactly solvable. This exact solution manifests as a non-linear recursion equation fulfilled by the expansion…
Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…
Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…
This article explores an operational model for transition amplitudes between measurements proposed by Goyal et al. within the quantum reconstruction program. To classify suitable amplitude algebras, we distinguish mathematical axioms,…
Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly…
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 comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including…
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles…
Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of dlog-forms with algebraic arguments, which in many cases can be evaluated in terms of multiple…
We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This…
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of…
We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this…