Light Through Matter: Quantum Mechanics & Complex Vectors

[forcefield]

I've been reading Feynman's (classical) derivation of the refractive index and I wonder if there is a more quantum mechanical description in terms of complex number field vectors - one vector for that part of light that goes straight through and another for that part of light that goes through accelerated charges - so that those component vectors are exactly at 90 degree angle with respect to each other so that total field vector is the sum of those component field vectors and if energy is proportional to square of field then total energy is also simply the sum of the energies of those component fields ?

(To clarify, I'm not asking about the refractive index but about the way that the field is divided between the part that goes straight through and the part that goes through accelerated charges).

 

[vanhees71]

That's called "quantum optics". My favorite textbook is

J. C. Garrison, R. Y. Chiao, Quantum Optics, Oxford University Press (2008)

 

[forcefield]

That's called "quantum optics".

Do you mean that within quantum physics "light through matter" is called "quantum optics" or that what I suggested is part of quantum optics ?

 

[vanhees71]

Quantum optics is, among other things, about the behavior of non-classical em.-field states with matter, among them also single-photon states. I understood your question in the way that you are asking for single-photon interactions with matter. As far as linear optics is concerned everything is more or less the same as in classical electromagnetism a la Maxwell, since in the linear approximation it doesn't matter too much, whether you deal with c-number fields (classical theory) or field operators (quantum field theory).

 

[forcefield]

I understood your question in the way that you are asking for single-photon interactions with matter.

Well, perhaps one can replace "part of light" in my OP with "photon"; but my question was about whether the light that reaches a point at the other side of matter can be represented with c-number fields that also represent probability amplitudes for part of light to either go straight through the matter or go through a charge that it accelerates.