Related papers: Notes on Motivic Periods
The first part of a set of notes based on lectures given at the IHES in May 2015 on Feynman amplitudes and motivic periods.
This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.
These are notes of lectures given at the CMI conference in August, 2014 at ICMAT in Madrid. The focus is on some mathematical questions associated to Feynman amplitudes, including Hodge structures, relations with string theory, and…
In fall of 2019, the Thursday Seminar at Harvard University studied motivic infinite loop space theory. As part of this, the authors gave a series of talks outlining the main theorems of the theory, together with their proofs, in the case…
We describe differential forms representing Feynman amplitudes in configuration spaces of Feynman graphs, and regularization and evaluation techniques, for suitable chains of integration, that give rise to periods of mixed Tate motives.
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…
Following the work of Brown, we can canonically associate a family of motivic periods -- called the motivic Feynman amplitude -- to any convergent Feynman integral, viewed as a function of the kinematic variables. The motivic Galois theory…
These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.
This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric…
Introduction to the Lecture Note Volume "ITEP Lectures in Particle Physics", including 25 years of personal reminiscences.
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…
Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…
These short lecture notes contain a not too technical introduction to point processes on the time line. The focus lies on defining these processes using the conditional intensity function. Furthermore, likelihood inference, methods of…
These lecture notes are meant to provide a pedagogical introduction, and present the latest theoretical and experimental developments on the physics of vortices in type II superconductors.
We study differential equations for Feynman amplitudes and we show that the corresponding D-module is isomorphic to a GKZ D-modules. We show that the sheaf of solutions to the D-module is isomorphic to a certain relative homology and the…
A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…
Brief recollections by the author about how he contributed to the production of the Feynman Lectures in Physics
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
These notes are the outgrowth of a series of lectures given at MSRI in January 1995 at the beginning of the special semester in complex dynamics and hyperbolic geometry. In these notes, the primary aim is to motivate the study of complex…
These notes are an account of a series of lectures given at the Les Houches Summer School "Active Matter and Non-equilibrium Statistical Physics" during August and September 2018. The lectures can be viewed online at…