Seminar: Epstein-Glaser in QED

Organizers: D.-A. Deckert, F. Merkl

Time & Location: Every Do 10-12, HS B 046

Abstract

In this seminar we will discuss the Epstein-Glaser approach to put the renormalization theory of perturbative quantum field theory on mathematical rigoros grounds. Generally speaking, here the word "perturbative" indicates that the theory starts with a formal expansion of the S-matrix. Order by order, the Epstein-Glaser approach then allows to infer well-defined summands of this expansion. The summability of these summands is not addressed. Nevertheless, the first few summands provide the well-known experimentally verified corrections to quantum theory. Particular emphasis will be laid on the external field model of QED, in which the Dirac sea is only subject to a prescribed external four-vector potential.

Topics overview

We will follow closely the G. Scharf's book (see below).

1. The scattering matrix in the Schrödinger theory on constant time hyperplanes; Chapter 0.3.
2. Perturbative scattering theory for QED; Chapter 3.1.
3. Method of splitting of causal distributions; Chapter 3.2.
4. Wick's Theorem; Chapter 3.3.
5. Vacuum polarization; Chapter 3.6.

Available Slides

1. A. Schaal: "Quantenmechanische Streutherie", Chapter 0.3. [PDF]

Literature

• Scharf. "Finite quantum electrodynamics." Berlin: Springer-Verlag, 1989.