What is the relationship between photons and electrons in quantum field theory?

[enzan]

I hear that the interaction between a photon and an electron is introduced by the local gauge invariance in the quantum field theory. On the other hand, I know that an decelerated electron emits a photon. Are these two saying the same thing? Or how these two are related?

 

[Demystifier]

The latter can be derived from the former, but not the vice versa.

 

[enzan]

Is a photon emission from an atom associated with an electron state transition also derived from the local gauge invariance?

 

[Demystifier]

Yes. The Schrödinger equation, which describes the electron, is also gauge invariant.

 

[enzan]

Does that mean that an electron state transition in an atom is described by a phase transformation of the electron field?
I'm asking this because I understand that the gauge transformation is a phase transformation.

 

[Demystifier]

Does that mean that an electron state transition in an atom is described by a phase transformation of the electron field?

No. The electron state transition is much more than a phase transformation.

 

[enzan]

What kind of gauge transformation (gauge invariance) is relevant to the electron state transition?

 

[bhobba]

What kind of gauge transformation (gauge invariance) is relevant to the electron state transition?

It isn't directly. It's handled as a perturbation:
http://www.tcm.phy.cam.ac.uk/~bds10/aqp/handout_dep.pdf

The full explanation requires QED which is much more difficult.

QED does depend crucially on gauge invariance - but again emissions of photons is handled by perturbation theory:
http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf

Thanks
Bill

 

[enzan]

I'm curious about what is the fundamental "principle" of photon emission (creation).
Can I safely say that the gauge invariance (or symmetry) is the one for any case, including a decelerated electron (Bremsstrahlung), Compton scattering, and the electron state transition in an atom?
Thank you.

 

[bhobba]

I'm curious about what is the fundamental "principle" of photon emission (creation)

Its tied up with the state of a quantum field is a Fock space:
http://en.wikipedia.org/wiki/Fock_space

Basically the question you are asking is not really meaningful in a Quantum Field Theory. A Quantum Field is a superposition of an unknown number of particles. The evolution of the field is basically an evolution of those unknown number of particles.

Symmetries more or less fix the form of a Quantum Field Theory - which is one of the great insights of modern physics. Gauge symmetry (also known as the symmetry of a circle) is the symmetry of EM. In and of itself its not responsible for particle creation, which is a rather subtle concept in QFT.

Thanks
Bill

 

[enzan]

Would it be possible to say something correctly about the fundamental principle of photon emission using words that can be understood by high school students?
For example, can I say that photon emission is always associated with a change of an electron's "state"?
Thank you.

 

[bhobba]

Would it be possible to say something correctly about the fundamental principle of photon emission using words that can be understood by high school students?.

No it wouldn't. Photons are described by Quantum Field Theory. And everything you have read outside a QFT textbook about it is likely wrong.

For high school students simply have some classes where they watch the master, Feynman, explain it:
http://www.vega.org.uk/video/subseries/8

And outside class read the book:
https://www.amazon.com/dp/0691024170/?tag=pfamazon01-20

And if a student asks what is the fundamental principle of photon emission - tell the truth - in the theory of such things - Quantum Field theory - there is no such principle. But its a very advanced theory and understanding how it explains such is beyond what can be explained at their level.

Thanks
Bill

 

[enzan]

I see. Thank you very much!

 

[Demystifier]

For example, can I say that photon emission is always associated with a change of an electron's "state"?

Yes, definitiely!

 

[Demystifier]

I'm curious about what is the fundamental "principle" of photon emission (creation).
Can I safely say that the gauge invariance (or symmetry) is the one for any case, including a decelerated electron (Bremsstrahlung), Compton scattering, and the electron state transition in an atom?
Thank you.

Theoretically, radiation could exist even without gauge invariance, but then some details of radiation could be somewhat different. For instance, the true radiation has only transversal polarization, while, without gauge invariance, radiation could also have longitudinal polarization.

 

[enzan]

Thank you very much for your comments!

 

[BillyT]

without getting too deep, it is worth while to note, that photons have length. I.e. the more well defined their energy is the more cycles they must contain and the less that can be said about the emission process due to the time energy precision limit of the uncertainty principle. For example, the green line photons from the northern lights are very precise in their energy - have so many cycles they are more than a meter long. And thus even "when" they were emitted is quite uncertain.

I have measured the length of some photons and shown one photon can in a classical sense be far (four feet) from itself! Here is how you do that:

Posting now below a crude "typed" drawing (in two parts):
Extended light source and lens making parallel beams (0nly one shown below) but each part of the source makes a beam at very slightly different angles:

*
*
*............()===== This beam enters beam splitter "a" shown below (this part of drawing separated for ease of construction.)
*
*

Ok, that is best I could do. (If I made lens () taller then parts of the light source, represented by some * , would be too far above or below lens.)
Below is one of the slightly divergent beams (only one shown), leaving the lens and going to first 45 degree beam splitter "a" and going straight thru with part (of same photon) going up to hit 45 degree mirror, b, too, which makes it again traveling parallel to the entering beam.
Sorry that these beam splitters and mirrors are not shown actually at 45 degrees - but that is best a "typed drawing" can do.

...........d
......b/======/======...This is the path of "self- rejoined" photon to the screen thru another lense one focal length from it.
......||......||
......||......||
......||......||
......||......||
()===== / ======/c
Lens.....a

Optically an "extended source" with lens one focal lengh from it followed by a second lense one focal length from the screen, just images the source (up side down) on the screen. Inserting these beam splitters and mirrors does not change that. It only make it possible for slightly differing path "split photons" to arrive at the screen where they would have but now they "want" to get back in phase with them selves, and do so as best a they can. Leaving dark lines where if they can not become "particles" there as they would not exist there since their waves are 180 degrees out of phase with themselves there. Note almost all the time photons can be thought of as waves, but if detected / absorbed they "die as particles" in one spot - not spread out over miles as they can be when waves.

Note that the length of paths: abd and acd, are the same. I.e. when the separate SINGLE photo get back together with itself, after being at times in its flight it 4 feet from itself, it arrives at the screen, unified, at the same time, but some of the many slightly divergent beams arriving there are "out of phase" with themselves and cancel (make dark interference lines) on the screen. The diverse in angle beams following paths abd & acd are exactly the same length ONLY for paths with pairs of equal angle degree corners. (parallelograms or rectangles.)

I will not go into details, but it is well known that photons ONLY interfere with themselves (and proven by using such low intensity sources that most of the time not even one exist - long exposure film, still has an interference pattern on the developed film, etc.) This is why one only needs monochromatic light, but not coherent light, source to produce interference patterns.

Now here is what you do to measure the length of a photon: You rotate beam splitter a very slightly counter clockwise, so that the path ab passes to the left of mirror at b, but pull mirror b back to still be hit by that now tilted beam. You of course must also rotate mirror b slightly clockwise, so the beam leaving it follows the old path to beam splitter d again. Now the corner turned at b is not 90 degrees. Perhaps this adds 5 cm of extra length to path abd.

What one sees on the screen is that there is a little light where there was none. I. e. the interference pattern on the screen is a little "washed out." This slight twisting of a & b is increased and then the pattern is more washed out. I kept repeating this until with ~30 cm extra path length for abd, the screen was with uniform illumination.

Crudely speaking this implies that none of the part of the photon going via path abd had yet arrived at the screen before the full length of the part of the same photon going by path acd had already disappeared into the screen. I.e. my spectral line source was making photons that were about 30cm long.

PS I have Ph. D. in physics and would be more active here, but my first post about time were removed as like this one I told things most do not know. Hope you get to read this one before it is removed.

 

[vanhees71]

Yes, definitiely!

Well, there are very interesting cases, where we observe photons, where no electrons are involved, like pion annihilation in a hot hadron gas or quark-gluon processes in the QGP (both created in heavy-ion collisions at various collision energies ranging from GSI (HADES experiment) via RHIC (STAR and PHENIX experiments; now also at a variety of beam energies up to top Au+Au collisions at $\sqrt{s}=200 A \text{GeV}$ to the LHC. For a theory perspective, see my lectures for graduate students:

http://fias.uni-frankfurt.de/~hees/hqm-lectweek14/index.html

For a shorter version for the Quark-Matter 2014 Student Day, see

http://fias.uni-frankfurt.de/~hees/publ/qm14-lect.pdf

 

[bhobba]

PS I have Ph. D. in physics and would be more active here, but my first post about time were removed as like this one I told things most do not know. Hope you get to read this one before it is removed.

I thought it was an excellent post. I don't think it will be removed.

Thanks
Bill

 

[yoron]

Interesting, as well as confusing (for me that is:), description BillyT. How do you think of it? As some practical limitation of a 'field concept', considering a 'particle', if I now would be so rude as to lend from Bhobba's " A Quantum Field is a superposition of an unknown number of particles. The evolution of the field is basically an evolution of those unknown number of particles."? Or, how would you prefer to describe it otherwise?

[Mentor's note - edited to remove text quoted from a removed post]

 

[bhobba]

if I now would be so rude as to lend from Bhobba's " A Quantum Field is a superposition of an unknown number of particles.

Single particle states exist. I was speaking in general. The picture of an electron emitting a photon is not correct.

Thanks
Bill

 

[yoron]

Yes, they do in the measurement. And I enjoyed your description :) so I lent from it. Because, to me then, somehow this 'length' of the particle also seems as depending on orientation of that measurement, possibly giving it an area, or volume if one like. Or maybe I'm wrong there? I don't know but I find it intriguing.

 

[bhobba]

Yes, they do in the measurement.

That's exactly it. The measurement will determine that.

Thanks
Bill

 

[yoron]

If you think of a photon as having a probability then, to exist when measured. would this length, if for example I by measurement defined it into a volume, have a relation to the photons probability of existing? Aka 'probability density'? Or? If I think of it as a length solely, then think of 'weak experiments' proving 'photon paths', then this becomes one description. If I ignore time, rotate this 'length' creating a 'area/volume' then there is another? If I can do it experimentally, in one try not ignoring time, it becomes even more intriguing to me. Ouch :)

 

[bhobba]

No - the length has to do with energy time relations.

What I am talking about is a quantum field being a Fock space, which is a superposition of a zero particle state, one particle state etc. A particle observation, like any quantum observation, gives no particles, one particle etc. But if its in a superposition then you don't know what the observation will result in. That's why the picture of an electron emitting a photon isn't correct.

If you know some QM its an extension of the harmonic oscillator:
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

Thanks
Bill

 

[yoron]

I think I get the idea bhobba, of your Fock space, but there's still something about this definition of a length, experimentally shown, that makes me wonder about it.

 

[bhobba]

I think I get the idea bhobba, of your Fock space, but there's still something about this definition of a length, experimentally shown, that makes me wonder about it.

The following may help:
http://www.math.ucr.edu/home/baez/uncertainty.html

Thanks
Bill

 

[yoron]

Thanks bhobba, I'm reading up on it. I can see the relation energy time, it's connected to the idea of 'virtual particles' too, isn't it?. But I still have to wrap my head around this, sort of :) What would the limit of length represent here for the photon?

 

[drjustian]

Very interesting thread. The question was asked and the responses were dependent upon the denomination of the person making the response, i.e., a field physicist or particle physicist. Can we hear from the loop and string folks too?

 

[Demystifier]

Well, there are very interesting cases, where we observe photons, where no electrons are involved

Of course. What I wanted to say is that whenever electron looses its energy, a photon is created. The reverse, of course, is not true.