Let's say you want to quantize the EM field in a system with real permittivities and permeabilities. You expand the fields into a superpositions of their classical modes, and note that pretty much every real spatial mode requires two real conjugate canonical variables to describe its time evolution. Then you quantize these variables in the usual way, and get oscillators out of them, along with the bosonic creation and annihilation operators. All of this works fine for the non-zero frequency fields, but fails on the zero-frequency field because it only requires one variable to describe its behavior: its amplitude. Is there a way to properly quantize static fields?