Positronium: Outline of the Theory*

Positronium is the lighest exotic atom and, in many ways, the simplest.  The structure of positronium is determined almost entirely by quantum electrodynamics (QED)--strong and weak interaction effects are minimal.  Positronium is also accessible to high-precision measurements.  Thus positronium serves as an important system for testing the limits of our understanding of QED bound state theory.

As in hydrogen, the motion of the constituents in positronium is nonrelativistic, so the states are, to lowest order, the same Schroedinger-Coulomb states as for hydrogen.  For increased accuracy, positronium can be described by the effective quantum field theory "NonRelativistic QED" (NRQED), which includes all corrections due to relativity and virtual particles.  Since its constituents are particle and antiparticle, positronium is also subject to annihilation.  Decay rates and distributions into two, three, or more photons can be calculated to high precision.  The states of positronium are eigenstates of the parity and charge conjugation symmetries, so detailed study of positronium decays can also serve as tests of these fundamental symmetries.

In this talk I will provide an overview of positronium physics and describe the current challenges facing theory, especially as regards ongoing and proposed experimental developments.