Quantum Brownian representation for the quantum field modes

When analyzing the particle-like excitations in quantum field theory it is natural to regard the field mode corresponding to the particle momentum as an open quantum system, together with the opposite momentum mode. Provided that the state of the field is stationary, homogeneous and isotropic, this scalar two-mode system can be equivalently represented in terms of a pair of quantum Brownian oscillators under a Gaussian approximation. In other words, the two-mode system behaves as if it were interacting linearly with some effective environment. In this paper we build the details of the effective linear coupling and the effective environment, and argue that this quantum Brownian representation provides a simple, universal and non-perturbative characterization of any single particle-like excitation. As immediate applications of the equivalence, we reanalyse the interpretation of the self-energy in terms of decay rates in a general background state, and present the master equation for the field mode corresponding to the particle momentum.