Nonlocal Quantum Field Theory and Quantum Entanglement

TL;DR

This paper explores a finite nonlocal quantum field theory that maintains key physical principles and uses it to analyze quantum entanglement entropy, demonstrating an area law free of UV divergences.

Contribution

It introduces a nonlocal quantum field theory framework that satisfies key invariances and causality, and applies it to compute entanglement entropy without UV divergences.

Findings

Entanglement entropy computed using NLQFT is UV finite.

The theory recovers the area law for entanglement entropy.

The nonlocal approach ensures causality and Poincaré invariance.

Abstract

We discuss the nonlocal nature of quantum mechanics and the link with relativistic quantum mechanics such as formulated by quantum field theory. We use here a nonlocal quantum field theory (NLQFT) which is finite, satisfies Poincar\'e invariance, unitarity and microscopic causality. This nonlocal quantum field theory associates infinite derivative entire functions with propagators and vertices. We focus on proving causality and discussing its importance when constructing a relativistic field theory. We formulate scalar field theory using the functional integral in order to characterize quantum entanglement and the entanglement entropy of the theory. Using the replica trick, we compute the entanglement entropy for the theory in 3 + 1 dimensions on a cone. The result is free of UV divergences and we recover the area law.