相关论文: Feynman Amplitudes and Cosmic Galois group

Efforts to understand and map the possible explanations for the late time acceleration of the universe have led to a broad range of suggestions, ranging from the cosmological constant and straightforward dark energy, to exotically coupled…

Galaxy groups constitute the most common class of galaxy systems in the known Universe, unique in terms of environmental properties. However, despite recent advances in optical and infrared observations as well as in theoretical research,…

I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…

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…

The talk consisted mainly in commenting in a linear way the seminal paper in 1964 by Michel Henon and graduate student Carl Heiles at Princeton University: "The applicability of the third integral of motion: Some numerical experiments" in…

Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…

We show that the spectrum of Kontsevich's algebra of formal periods is a torsor under the motivic Galois group for mixed motives over the rational numbers. This assertion is stated without proof by Kontsevich and originally due to Nori. In…

We utilize a mass independent Klein-Gordon equation that is first order in a variable that plays the role of time, the approach taken in parametric time formulations. Using concepts from semigroup evolution, we examine the sign of a noisy…

A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological…

In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. This is followed by lectures on important…

We show that, by using amplitude-based resummation techniques for Feynman's formulation of Einstein's theory, we get quantum field theoretic 'first principles' predictions for the UV fixed-point values of the dimensionless gravitational and…

This article summarizes the talks in the session GW2 of the Sixteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, 5-10 July, 2021, on…

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

In the mid sixties, A. Grothendieck envisioned a vast generalization of Galois theory to systems of polynomials in several variables, motivic Galois theory, and introduced tannakian categories on this occasion. In characteristic zero,…

These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.

This lecture note is written for 'Courses on Light-Cone Techniques applied to QCD', Nov 21-25, 2022, IGFAE. It is intended to provide basic knowledge and selective perspectives on the application of light-front Hamiltonian approach to…

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…

These lecture notes collect the material that I have been using over the years for various short courses on the physics of gravitational waves, first at the Institut d'Astrophysique de Paris (France), and then at SISSA (Italy) and various…

We discuss a remarkable new approach initiated by Cachazo, Svrcek and Witten for calculating gauge theory amplitudes. The formalism amounts to an effective scalar perturbation theory which in many cases offers a much simpler alternative to…

This paper is based on the rapporteur talk given at the 34$^{th}$ International Cosmic Ray Conference (ICRC), on August 6$^{th}$, 2015. The purpose of the talk and paper is to provide a summary of the most recent results from balloon-borne…