Open Effective Field Theories from Highly Inelastic Reactions

TL;DR

This paper develops a framework for incorporating highly inelastic reactions into effective field theories by deriving a Lindblad equation for the effective density matrix, accounting for particle loss and high-momentum states.

Contribution

It introduces a method to modify the density matrix evolution in effective field theories to include inelastic reactions via Lindblad operators, extending previous approaches.

Findings

Effective density matrix satisfies Lindblad equation.

Lindblad operators are determined by anti-Hermitian terms.

Framework accounts for high-momentum particle states.

Abstract

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.