Related papers: Notes on Motivic Periods
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
A theory of 'time' as a form of 'information' is proposed. New tools such as Feynman Clocks, Collective Excitation Networks, Sequential Excitation Networks, Plateaus of Complexity, and Causal Networks are used to unify previously separate…
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
Assorted questions: Time as a parameter in Quantum Mechanics. No-Go theorems for a time operator. Localization, time and causality. Causality violation. Localization again. Lesson 1: Evading the troubles: Im E finite. Lights and shadows of…
This brief and opinionated essay evolved from my closing talk at the Tenth International Workshop on Neutrino Telescopes, held in Venice in March 2003. Portions were inspired by several excellent presentations at the Workshop. Other…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
We use mixed Hodge structures to investigate Feynman amplitudes as functions of external momenta and masses.
Given two smooth projective varieties X and Y over a field, we say that X motivates Y if the (suitably defined) motive of Y is contained in the category generated from X by taking sums, summands and products. This notion has appeared…
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
Using the newly modified method developed for symbolic evaluation of Feynman amplitudes we examine two processes $2\to 2$ (including a case of Majorana fermions) at a tree level. Constructing special polarization basis for spinor particles,…
In this paper we study motivic amplitudes--objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to…
The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be…
This reply addresses concerns expressed in a comment (arXiv:2508.16689v1) on arXiv:submit/6841332 [physics.gen-ph] 29 Sep 2025 the paper given in the title (arXiv:2501.02022v2), hereafter referred to as the paper.
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…
Summary talk at ICHEP 2002, Amsterdam, July 2002. I have kept very close to the content and style of the talk as it was delivered. You may access the associated PowerPoint presentation through a link at…
Notes to lectures on the epsilon calculus, covering axioms, semantics, completeness, and the first epsilon theorem.
Recently introduced model of magnetic hysteresis was extended into set of the following features: frequency, pick of induction and temperature of specimen. Group theoretical classification of hysteresis loops' sets is presented. An effect…
These informal lecture notes describe the progress in semiconductor spintronics in a historic perspective as well as in a comparison to achievements of spintronics of ferromagnetic metals. After outlining motivations behind spintronic…