Can the polarization bound charge density be expressed in vacuum by a wave function?

[south]

TL;DR

I ask the question assuming that vacuum polarization does not always require the presence of large potentials or large energy densities.

Can the polarization bound charge density be expressed in vacuum by a wave function?

 

[DrDu]

Maybe you can give some more background on your question. In vacuum, there are no bound charges. So it is not clear what you mean.

 

[south]

Thanks DrDu for your help. I'll try to expand.

Nothing practical. Just theory. Monochromatic plane EM wave propagating in vacuum. The wave equation in this case admits a sinusoidal solution, a cosinusoidal solution, and a complex exponential solution.

In EM propagation, the electric field $$\vec{E}$$, the magnetic field $$\vec{B}$$, and other fields, such as the electric displacement $$\vec{D}$$, which interests me particularly, undulate.

When there is no circular or elliptical polarization, the wave equations of $$\vec{E}$$ and $$\vec{B}$$ do not admit the complex exponential solution. Does the wave of the field $$\vec{D}$$ admit this solution?

The answer depends on considering vacuum polarization impossible or possible for any frequency greater than zero. Vacuum disruptive polarization does not occur at any frequency. And what about a non-disruptive polarization, let's say linear harmonic polarization?

I don't dare to deny in advance the possibility of a linear harmonic polarization of the vacuum, without analyzing the subject carefully and in sufficient detail.

 

[renormalize]

When there is no circular or elliptical polarization, the wave equations of $\vec{E}$ and $\vec{B}$ do not admit the complex exponential solution. Does the wave of the field $\vec{D}$ admit this solution?

Why do you believe this is true? Can you prove it? What exactly do you think the difference is between $\vec{D}$ and $\vec{E}$ in vacuum?

Vacuum disruptive polarization does not occur at any frequency. And what about a non-disruptive polarization, let's say linear harmonic polarization?

Please define "disruptive polarization" and "non-disruptive polarization".

 

[south]

Why do you believe this is true? Can you prove it? What exactly do you think the difference is between $\vec{D}$ and $\vec{E}$ in vacuum?

Please define "disruptive polarization" and "non-disruptive polarization".

The conversation has veered into demands that are beyond my reach. I beg your pardon for not being able to continue. Thank you very much and best regards.