Entanglement, Renormalization and Effective Field Theories

TL;DR

This paper explores how entanglement in momentum space underpins renormalization and effective field theories, demonstrating a method to derive low-energy theories from high-energy quantum field models.

Contribution

It introduces a novel perspective linking entanglement to renormalization, providing a perturbative approach to construct effective theories and derive renormalization group equations.

Findings

Successful decoupling of modes using unitary transformations

Consistent implementation of renormalization in scalar field models

Derivation of a renormalization group equation within this framework

Abstract

We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an interacting quantum field theory. Using unitary transformations to decouple these modes at the perturbative level, we show in a scalar field theoretical model with light and heavy fields, how renormalization may be consistently implemented and how the low energy effective field theory can be constructed. We also obtain a renormalization group equation in this framework and apply it to the scalar field theoretical model.