Coarse graining and decoherence in quantum field theory

TL;DR

This paper investigates how integrating out short-wavelength modes in a quantum field theory leads to decoherence of long-wavelength modes, with implications for quantum-to-classical transition in cosmological settings.

Contribution

It introduces a method to derive a coarse-grained effective action and master equation for decoherence in quantum field theory, extending to curved spacetime.

Findings

Decoherence is effective when the critical wavelength exceeds the Hubble radius.

Derived diffusion coefficients quantify the decoherence process.

The approach applies to both Minkowski and DeSitter spacetimes.

Abstract

We consider a $\lambda \phi^4$ theory in Minkowski spacetime. We compute a "coarse grained effective action" by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients of this equation and analyze the decoherence induced on the long- wavelength modes. We generalize the results to the case of a conformally coupled scalar field in DeSitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius.