  On the basis of macroscopic quantum electrodynamics, a theory of Casimir
forces in the presence of on linearly amplifying bodies is presented which
provides a consistent framework for studying the effect of, e.g., amplifying
left-handed metamaterials on dispersion forces. A general formula for the
Casimir force acting on an amplifying body is derived. It is shown that the
force can be given in terms of the classical Green tensor and that it can be
decomposed into a resonant component associated with emission processes and an
off-resonant Lifshitz-type component looking formally the same as for a purely
absorbing body. It is explicitly demonstrated that the result generalizes
microscopic approaches beyond the perturbative domain: In the dilute-gas limit,
the force acting on an amplifying body reduces to a sum over the
Casimir--Polder forces acting on the excited body atoms.
