00:00:00 / 00:00:00

Renormalization Hopf Algebras and Gauge Theories

By Walter Van Suijlekom

Appears in collection : Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

We give an overview of the Hopf algebraic approach to renormalization, with a focus on gauge theories. We illustrate this with Kreimer's gauge theory theorem from 2006 and sketch a proof. It relates Hopf ideals generated by Slavnov-Taylor identities to the Hochschild cocycles that are given by grafting operators.

In the second part of the talk I will briefly present Kreimer's unexpected influence on noncommutative geometry via my more recent research. In joint work with Teun van Nuland we uncover a rich structure of the spectral action functional. We express its Taylor expansion in an inner perturbation in terms of Yang-Mills and Chern-Simons forms integrated against even Hochschild and odd cyclic cocycles, respectively.

Information about the video

  • Date of recording 16/11/2020
  • Date of publication 29/11/2020
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

Document(s)

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback