  The loss of particles due to highly inelastic reactions has previously been
taken into account in effective field theories for low-energy particles by
adding local anti-Hermitian terms to the effective Hamiltonian. An additional
modification is required in the time evolution equation for the density matrix
of a multi-particle system. An effective density matrix can be defined by
tracing over states containing high-momentum particles produced by the highly
inelastic reactions and by a time average that eliminates short-time
correlations. The effective density matrix satisfies the Lindblad equation,
with local Lindblad operators that are determined by the anti-Hermitian terms
in the effective Hamiltonian.
