  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.
