The Ehrenfest Theorem in Quantum Field Theory

TL;DR

This paper investigates the applicability of Ehrenfest's theorem within Abelian and non-Abelian quantum field theories, demonstrating its validity under unbroken gauge symmetries by selecting an appropriate physical subspace.

Contribution

It proves the validity of Ehrenfest's theorem in both Abelian and non-Abelian quantum field theories with unbroken gauge symmetries through a specific choice of physical subspace.

Findings

Ehrenfest's theorem holds in Abelian QFTs with unbroken gauge symmetry.

Ehrenfest's theorem holds in non-Abelian QFTs with unbroken gauge symmetry.

A suitable physical subspace ensures the theorem's validity.

Abstract

The validity of the Ehrenfest's theorem in Abelian and non-Abelian quantum field theories is examined. The gauge symmetries are taken to be unbroken. By suitably choosing the physical subspace, the above validity is proven in both the cases.