Quantising one-dimensional electromagnetic fields in position space

An intuitive and straightforward modelling of many locally-interacting quantum system requires a local description of the quantised electromagnetic field. In a recent paper [Southall et al., J. Mod. Opt. 68, 647 (2021)], we showed that such a description, which must overcome several no-go theorems, is indeed possible. To better justify our approach, this paper presents a systematic quantisation of one-dimensional electromagnetic fields in position space. Starting from the assumption that its basic building blocks are local bosonic particles with a clear direction of propagation--so-called bosons localised in position (BLiPs)--we identify the relevant Schroedinger 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 monochromatic photon Fock states.