Related papers: Four Lectures on Euler Integrals
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
We introduce a new approach for the computation of the class of Feynman integrals whose integrands vanish in strictly four-dimensions, so-called ''pseudo-evanescent'' integrals. We argue that, up to $\mathcal{O}(\epsilon)$ corrections,…
We present a subtraction scheme for ultraviolet (UV) divergent, infrared (IR) safe scalar Feynman integrals in dimensional regularization with any number of scales. This is done by the introduction of $u$-variables, which are a suitable…
The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
The most commonnly used methods of the theoretical analysis of electromagnetic oscillations and waves are described. The lectures are given for the fourth-year students of Moscow Institute of Physics and Technology. These lectures can be…
These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…
Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory.…
The role of hyperlogarithms and multiple zeta values (and their generalizations) in Feynman amplitudes is being gradually recognized since the mid 1990's. The present lecture provides a concise introduction to a fast developing subject that…
We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…
We describe an algorithm to organize Feynman integrals in terms of their infrared properties. Our approach builds upon the theory of Landau singularities, which we use to classify all configurations of loop momenta that can give rise to…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel…
The subject of our discussion is the theory of differential equations as set out in two classical Euler's textbooks "Institutiones Calculi Differentialis" and "Institutiones Calculi Integralis".
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the…
Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function $Li_(z)$. The…
I give a brief introduction to particle interactions based on representations of Poincare Lie algebra. This is later generalized to interactions based on representations of the supersymmetry Lie algebra. Globally supersymmetric models with…
Integration by parts is used to reduce scalar Feynman integrals to master integrals.
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…