Quantum renormalization group

TL;DR

This paper explores how entanglement between IR and UV particles in a regulated quantum field theory affects the IR sector's description, deriving a renormalized trajectory considering mixed states and the necessity of a sharp cutoff.

Contribution

It introduces a method to derive the tree-level renormalized trajectory for a self-interacting scalar field, accounting for mixed state contributions due to entanglement.

Findings

IR and UV particles are entangled via interactions in cutoff theories.

The IR sector can be described by a density matrix due to this entanglement.

A sharp cutoff is necessary to observe true information loss.

Abstract

The observed IR and the spectator UV particles of a regulated, cutoff quantum field theory are entangled by their interactions; hence, the IR sector can be described by the help of the density matrix only. The tree-level renormalized trajectory is obtained for a self-interacting scalar field theory, containing the mixed state contributions. One needs a sharp cutoff in the momentum space as regulator to realize the true loss of information, caused by massive particles.