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We extend Gegenbauer Polynomials technique to evaluate a class of complicated Feynman diagrams. New results in the form of $_3F_2$-hypergeometrical series of unit argument, are presented. As a by-product, we present a new transformation…
We present a study of the structure of phase diagrams for matter-radiation systems, based on the use of coherent states and the catastrophe formalism, that compares very well with the exact quantum solutions as well as providing analytical…
One problem which plagues the numerical evaluation of one-loop Feynman diagrams using recursive integration by part relations is a numerical instability near exceptional momentum configurations. In this contribution we will discuss a…
We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the…
Feynman diagrams are calculated by means of their Taylor series expansion in terms of external momenta squared. It is demonstrated in various examples that by the application of conformal mapping and Pad\'{e} approximants, it is possible to…
We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…
We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…
We propose a decision criterion for segmenting the cosmic web into different structure types (voids, sheets, filaments, and clusters) on the basis of their respective probabilities and the strength of data constraints. Our approach is…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…
We give a short introduction to Feynman diagrams, with many exercises. Text is targeted at students who had little or no prior exposure to quantum field theory. We present condensed description of single-particle Dirac equation, free…
Introductory lectures on the phenomenology of the minimal supersymmetric Standard Model. The emphasis is on general signatures for supersymmetry and on the motivation for constructing supersymmetric models. These lectures are intended for…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…
These lectures introduce some of the basic methods of perturbative QCD and their applications to phenomenology at high energy. Emphasis is given to techniques that are used to study QCD and related field theories to all orders in…
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
Mellin-Barnes and sector decomposition methods are used to evaluate tensorial Feynman diagrams in the Euclidean kinematical region. Few software packages are shortly described and few examples demonstrate their use.
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…