Polyelectrons are bound states of a few electrons and positrons. The
simplest example is positronium. Its negative ion (two electrons and
a positron), as well as a four-body dipositronium molecule have also
been discovered and are subject of ongoing experiments. Among their
goals is the creation of larger polyelectrons to study the
Bose-Einstein condensation of positronia and a gamma ray laser based
on stimulated annihilation.
In this talk I will review effective field theory methods used to
determine precise properties of three- and four-body polyelectrons.
I will also show other examples of how exotic atoms provide information
about fundamental interactions, and how methods originating in
high-energy theory help determine their properties.