Related papers: A simple way to generate high order vacuum graphs
We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
Both the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism are central tools for analyzing primordial cosmological observables, such as equal-time correlation functions. While their conceptual equivalence is well…
I present results for the two-loop self-energy functions for scalars in a general renormalizable field theory, using mass-independent renormalization schemes based on dimensional regularization and dimensional reduction. The results are…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the…
This text reviews, hopefully in a pedagogical manner, a series of work on the automatic calculations of Feynman diagrams in the context of quantum nanoelectronics (Keldysh formalism) with an application to the Kondo effect in the…
A well-known problem in Algebraic Combinatorics, is the enumeration of circulant graphs. The failure of Adam's Conjecture for such graphs with order containing a repeated prime, led researchers to investigate the problem using two different…
The obstruction for application of effective techniques like denominator reduction for the computation of the $c_2$ invariant of Feynman graphs in general is the absence of a 3-valent vertex for the initial steps. In this paper such a…
The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for…
Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This…
Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
The combinatorial refinement techniques have proven to be an efficient approach to isomorphism testing for particular classes of graphs. If the number of refinement rounds is small, this puts the corresponding isomorphism problem in a…
We review the combinatorial structure of perturbative quantum field theory with emphasis given to the decomposition of graphs into primitive ones. The consequences in terms of unique factorization of Dyson--Schwinger equations into Euler…
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of…
For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The…
We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…