Lubos Motl , a member of this site, has a blog entry on how the classical fields emerge from QFT.
From the introduction :
I will discuss two somewhat different situations which however cover almost every example of a classical logic emerging from the quantum starting point:
- Classical coherent fields (e.g. light waves) appearing as a state of many particles (photons)
- Decoherence which makes us interpret absorbed particles as point-like objects and which makes generic superpositions of macroscopic objects unfit for well-defined questions about classical facts
However, in the rest of this section, I want to focus on another way how to see classical physics of fields emerge out of large ensembles of photons, one that mimics the thermodynamic limit of statistical physics (even in the context of classical mechanics).
for me the crux of the argument lies in the observation
The photons also have polarizations so the wave function has many components, too. I don't want to scare you by the indices but the wave function of a single photon mathematically looks like the (complexified) classical electromagnetic potential A⃗ (x,y,z), with some extra subtleties. (But its interpretation is different!)
which connects the classical electromagnetic field with the individual photons.
One does not need to carry the cumbersome ensemble of photons in discussing macroscopic observations as, for example, reflections, scattering of light and optical ray drawings. It is enough that it is possible to do so, but it is much more convenient to use the classical version, as we use thermodnamics, and not statistical mechanics, when discussing the behavior of matter in bulk, though there exists a one to one correlation of the microscopic mechanics to the macroscopic emergent variables and distributions.