  Positronium decay into a muon-antimuon pair by virtue of the interaction with
a superintense laser field of linear polarization is considered. The minimum
laser intensity required amounts to a few 10^22 W/cm^2 in the near-infrared
frequency range. Within the framework of laser-dressed quantum electrodynamics,
the total reaction rate is calculated and related to the cross section for
field-free electron-positron annihilation into muons. The muons are created
with ultrarelativistic energies and emitted under narrow angles along the laser
propagation direction. The dynamical properties of the muons are interpreted in
terms of a classical simple man's model for the production process. We show
that the most promising setup for an experimental investigation of the process
employs two counterpropagating laser beams impinging on a positronium target,
where the advantage of the coherent electron-positron collisions becomes
evident.
