Classical limits of unconstrained QFT

TL;DR

This paper explores how unconstrained quantum field theories behave in nonrelativistic limits, showing that their states follow Newtonian trajectories with $1/r^2$ forces, including bound states.

Contribution

It demonstrates that in certain limits, unconstrained QFT states evolve according to classical Newtonian dynamics, extending understanding of quantum-classical correspondence.

Findings

States follow Newton's equations in nonrelativistic limits

Bound solutions exist for attractive forces

Quantum field states approximate classical trajectories

Abstract

In nonrelativistic limits for states labeled by minimum packets with constrained spatial spreads and over a short term, states of unconstrained quantum field theories evolve on trajectories described by Newton's equations for the $1/r^2$ force. These states include bound solutions in the attractive force case.