  An elementary field-theoretic mechanism is proposed that allows one
Lagrangian to describe a family of particles having different masses but
otherwise similar physical properties. The mechanism relies on the observation
that the Dyson-Schwinger equations derived from a Lagrangian can have many
different but equally valid solutions. Nonunique solutions to the
Dyson-Schwinger equations arise when the functional integral for the Green's
functions of the quantum field theory converges in different pairs of Stokes'
wedges in complex field space, and the solutions are physically viable if the
pairs of Stokes' wedges are PT symmetric.
