  We propose a solution to the problem of Bloch electrons in a homogeneous
magnetic field by including the quantum fluctuations of the photon field. A
generalized quantum electrodynamical (QED) Bloch theory from first principles
is presented. In the limit of vanishing quantum fluctuations we recover the
standard results of solid-state physics, for instance, the fractal spectrum of
the Hofstadter butterfly. As a further application we show how the well known
Landau physics is modified by the photon field and that Landau polaritons
emerge. This shows that our QED-Bloch theory does not only allow to capture the
physics of solid-state systems in homogeneous magnetic fields, but also novel
features that appear at the interface of condensed matter physics and quantum
optics.

Mesoscale and Nanoscale Physics;Materials Science