Bound states  from QED to QCD
Abstract
These lectures are divided into two parts. In Part 1 I discuss bound state topics at the level of a basic course in field theory: The derivation of the Schrödinger and Dirac equations from the QED Lagrangian, by summing Feynman diagrams and in a Hamiltonian framework. Less well known topics include the equaltime wave function of Positronium in motion and the properties of the Dirac wave function for a linear potential. The presentation emphasizes physical aspects and provides the framework for Part 2, which discusses the derivation of relativistic bound states at Born level in QED and QCD. A central aspect is the maintenance of Poincaré invariance. The transformation of the wave function under boosts is studied in detail in D=1+1 dimensions, and its generalization to D=3+1 is indicated. Solving Gauss' law for $A^0$ with a nonvanishing boundary condition leads to a linear potential for QCD mesons, and an analogous confining potential for baryons.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5005
 Bibcode:
 2014arXiv1402.5005H
 Keywords:

 High Energy Physics  Phenomenology;
 Nuclear Theory
 EPrint:
 45 pages. Lectures presented at the "Minischool on theoretical methods in particle physics" at the Higgs Centre for Theoretical Physics, University of Edinburgh on 30 September to 4 October 2013. Comments are welcome