Momentum-space entanglement and renormalization in quantum field theory

TL;DR

This paper explores the entanglement structure of quantum field theories in momentum space, relating it to the Wilsonian effective action and proposing entanglement measures as natural observables for understanding scale-dependent phenomena.

Contribution

It establishes a connection between momentum-space entanglement entropy and the Wilsonian effective action, introducing entanglement measures as tools for analyzing scale separation in quantum field theories.

Findings

Derived a relation between entanglement entropy and the Wilsonian effective action.

Proposed entanglement entropy and mutual information as natural observables in QFT.

Showed that entanglement decay relates to decoupling in quantum field theory.

Abstract

The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation between this density matrix and the conventional Wilsonian effective action. We argue that the entanglement entropy of and mutual information between subsets of field theoretic degrees of freedom at different momentum scales are natural observables in quantum field theory and demonstrate how to compute these in perturbation theory. The results may be understood heuristically based on the scale-dependence of the coupling strength and number of degrees of freedom. We measure the rate at which entanglement between degrees of freedom declines as their scales separate and suggest that this decay is related to the property of decoupling in quantum field theory.