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

Open Effective Field Theories from Highly Inelastic Reactions