Dispersive medium as a field

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I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?
 

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Andy Resnick
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I am studying phase and group velocity in non-dispersive and dispersive media. My question is the following: Is there any reason why a dispersive medium simply cannot be modeled as a type of field?
Typically, a medium is modeled in terms of a constitutive relationship between two fields (E and D, B and H, stress and strain, etc.) rather that a field itself. The downside is that there is a fundamentally phenomenological aspect to constitutive relationships, but the upside is that the modeling framework can be very general.
 
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vanhees71
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Well, a bit more ambitious is to calculate the constitutive relationships from the underlying microscopic dynamics of the matter interacting with the em. field. The methods reach from classical transport models to the full quantum theortical treatment. One flavor of the latter case is the use of the Kadanoff-Baym equations which entirely are based on quantum field theory (not necessarily relativistic; in condensed-matter physics you use non-relativistic QFT for that purpose) to derive them.

In the usual textbook case you use matter close to thermal equibrium to derive the permittivity, permeability, and electric conductivity in "linear-response approximation" making use of the Green-Kubo relations.
 

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