Quantizing Zero-Frequency Modes: A Challenge

[Manchot]

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?

 

[QuantumBend]

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?

You speaking many virtual photon zero frequency no energies, or another one? Analyszing Fourier Transforms (for ZERO only - not many) give the field. Yes, this need mathematic, No initial final Not in foam - I know this.

OR:

Field not there when no observers. Only probables do you mean this?.

 

[Manchot]

^ I didn't quite understand what you meant. To be clearer, I'm referring to the zero-frequency classical modes, i.e., the static solutions of Maxwell's equations. If you try to quantize them in the same way that you quantize the other modes, you fail because they only require one canonical variable to describe them and can't be described by Hamilton's equations. I'm wondering how to get around this.