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 equal-time 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 non-vanishing boundary condition leads to a linear potential for QCD mesons, and an analogous confining potential for baryons.

45 pages. Lectures presented at the "Mini-school 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

References in corpus (4)

• Hyperfine splitting in positronium to $\mathcal{O}({\alpha }^7{m}_e)$: one-photon annihilation contribution
• States of the Dirac equation in confining potentials
• Towards a Born term for hadrons
• Positronium contribution to the electron g-2

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• Dark Matter Bound State Formation in Fermionic $Z_2$ DM model with Light Dark Photon and Dark Higgs Boson
• Selection Rule for Enhanced Dark Matter Annihilation
• Nucleon - Nucleon Interactions at Short Distances
• Lectures on Bound states
• Gravitino condensation, supersymmetry breaking and inflation