Understanding Light Propagation for Quantum Field Theory

[captain]

do you need to know about the propagation of light to understand quantum field theory?

note: when i speak of propagation of light i am only talking about these topics only: geometrical optics, intensity, the angular eikonal, narro bundles of rays, image formation with broad bundles of rays, limits of geometrical optics, diffraction, fresnel diffraction, fraunhofer diffraction.

 

[genneth]

They have no direct relevance to the foundations of quantum field theory. However, it's important whilst studying QFT to understand how those various phenomenon are accounted for.

 

[mjsd]

the one most important thing about the propagation of light that is relevant to QFT is the fact that speed of light is a "constant".. ie. special relativity.

 

[captain]

thanks for your responses

 

[captain]

does the radiation of electromagnetic waves have anything to do with quantum field theory?

note: when i speak of radiation of electromagenetc waves i am only referring to the topics: the field of a system of charges at large distances, dipole radiation, dipole radiation during collisions, radiation of low frequency in collision, radiation in the case of coulomb interaction, quadrupole and magnetic dipole radiation, the field of the radiation at near distances, radiation from a rapidly movig charge, synchrotron radiation (magnetic bremsstrahlung), radiation damping, radiation damping in the relativistic case, spectral resolution of the radiation in the ultrarelativistic case, scattering by free charges, scattering of low frequency waves, scattering of high frequency waves.

 

[mjsd]

I am sure they do, but how exactly everything ties together, I am not qualified to tell you that. remember, QFT comes from special rel + QM... and so such "action-at-a-distance" can naturally be explained by QFT.

eg. in the QFT picture, electromagnetic interactions are mediated by virtual photons (like a messager).. so for instance a +ve charge knows a presence of -ve charge nearby because of the exchange of these virtual photons between them. but of course real radiation are carried by real photons.

 

[genneth]

does the radiation of electromagnetic waves have anything to do with quantum field theory?

note: when i speak of radiation of electromagenetc waves i am only referring to the topics: the field of a system of charges at large distances, dipole radiation, dipole radiation during collisions, radiation of low frequency in collision, radiation in the case of coulomb interaction, quadrupole and magnetic dipole radiation, the field of the radiation at near distances, radiation from a rapidly movig charge, synchrotron radiation (magnetic bremsstrahlung), radiation damping, radiation damping in the relativistic case, spectral resolution of the radiation in the ultrarelativistic case, scattering by free charges, scattering of low frequency waves, scattering of high frequency waves.

In so far as they're both models of the same phenomenon, yes. In so far as whether courses that teach them will cover that material, no. Whole field effects in QED are given by coherent photon states, and usually people don't bother to actually base their calculations on them. The usual testing ground of QED is high energy particle collisions, where you have a tiny space over which interactions occur, and detection (and set-up) is done at approximately infinity away.

 

[Slaviks]

does the radiation of electromagnetic waves have anything to do with quantum field theory?

Your question is quite broad, I'd just like to comment that QFT is about the ways to solve for quantum mechanical behaviour of a system with an infinite number of degrees of freedom (a field), whenever such physical model is applicable. It by no mean has to deal with electromagnetism (that is, QED is just application of QFT to electrodynamics). You can study QFT using, e.g. field theories for phase-transitions in condensed matter systems.

 

[belliott4488]

Another note: from a quick look, it looks to me as if all the E-M phenomena you referred to are classical, which means that they can be explained by the Maxwell Eqs. For that reason, they follow from QFT, specifically QED, once you see how the Maxwell Eqs. follow from the theory. For that reason they don't need to come up explicitly.

On the other hand, it should be possible to explain all those phenomena in purely QFT terms, if one had a good reason to do so, although I'm certainly not about to try!

 

[captain]

Your question is quite broad, I'd just like to comment that QFT is about the ways to solve for quantum mechanical behaviour of a system with an infinite number of degrees of freedom (a field), whenever such physical model is applicable. It by no mean has to deal with electromagnetism (that is, QED is just application of QFT to electrodynamics). You can study QFT using, e.g. field theories for phase-transitions in condensed matter systems.

just a quick question, is the number of degrees of freedom the same as the number to dimensions in hilbert space for the specific state of a field?

 

[genneth]

just a quick question, is the number of degrees of freedom the same as the number to dimensions in hilbert space for the specific state of a field?

I'll say that it is. Unfortunately, of course, it's not *really* that simple.

 

[Slaviks]

just a quick question, is the number of degrees of freedom the same as the number to dimensions in hilbert space for the specific state of a field?

Not really. The number of degree of freedoms of a free bosonc is the number of Harmonic oscillators you use to describe it. Formally it is divergent, but physically you always have a small-k cutoff. But then even for a single harmonic oscialltor, the corresponding Hilber space has infinite number of dimensions (again, usually one can truncate at highenough energies).
So the total dimension of the Hilbert space for a specific state
is one large numebr (the number of oscillators) to the power of another large numebr (the number of sates of a single oscillator.

In this way you can see why quantum field theory is much "richer" that the its calssical limit: in the classical limit, each oscillator is characterized by a single number (amplitude), while the quantum description assigns to it an infinitely-dimensional vector.