Testing Hamiltonian Reduced QED

TL;DR

This paper investigates the differences between conventional QED and a Hamiltonian reduced version, revealing an experimentally detectable electric Aharonov-Bohm effect absent in the reduced theory, with implications for quantum interference and gravity.

Contribution

It demonstrates that the Hamiltonian reduced QED predicts no electric Aharonov-Bohm effect, unlike conventional QED, and proposes an experimental test to distinguish between them.

Findings

Conventional QED predicts an electric Aharonov-Bohm effect.

Hamiltonian reduction eliminates the electric Aharonov-Bohm effect.

Experimental test using superconducting quantum interferometry can distinguish the theories.

Abstract

Certain gauge transformations may act non-trivially on physical states in quantum electrodynamics (QED). This observation has sparked the yet unresolved question of how to characterize allowed boundary conditions for gauge theories. Faddeev and Jackiw proposed to impose Gauss' law on the action to find the Hamiltonian reduced theory of QED. The reduction eliminates the scalar gauge mode, renders the theory manifestly gauge invariant and the symplectic form non-singular. In this work we show that while the predictions of the reduced theory coincide with those of conventional QED for scattering events, it is experimentally distinguishable. Quantum interference of charges traveling along time-like Wilson loops that encircle (but remain clear of) electric fields is sensitive to a relative phase shift due to an interaction with the scalar potential. This is the archetypal electric Aharonov-Bohm effect and does not exist in the reduced theory. Despite its prediction over six decades ago, and in contrast to its well known magnetic counterpart, this electric Aharonov-Bohm phenomenon has never been observed. We present a conclusive experimental test using superconducting quantum interferometry. The Hamiltonian reduction renders a theta term non-topological. We comment on consequences for semi-classical gravity, where it may alleviate a problem with the measure.