Local photons

TL;DR

This paper demonstrates a local quantum description of electromagnetic fields supporting localized photon wave packets, overcoming no-go theorems, and connecting to standard quantum electrodynamics.

Contribution

It introduces a local field framework based on bosons localized in position, providing a Lorentz-covariant formulation that aligns with traditional QED.

Findings

Supports localized photon wave packets in a quantum framework

Constructs Lorentz-covariant electric and magnetic field observables

Reduces to standard QED in a specific subspace

Abstract

The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all times. Motivated by this observation, this paper builds on recent work by Southall et al. [J. Mod. Opt. 68, 647 (2021)] and shows that a local description of the quantised electromagnetic field, which supports such solutions and which must overcome several no-go theorems, is indeed possible. Starting from the assumption that the basic building blocks of photonic wave packets are so-called bosons localised in position (blips), we identify the relevant Schr\"odinger equation and construct Lorentz-covariant electric and magnetic field observables. In addition we show that our approach simplifies to the standard description of quantum electrodynamics when restricted to a subspace of states.