Exploring the Completeness of QED: An Introduction to Quantum Electrodynamics"

[nlsherrill]

First off, I am very ignorant to this subject. I am only a rising sophomore in physics and have not taken any "modern" physics courses yet(but will in the fall).

So I have heard/read that quantum electrodynamics is the more accurate scientific theory to date. Is this theory "complete"? It seems like whenever I look around at areas of study in QFT, I always see QCD and never hear about research still being done in QED. Is electromagnetism fully understood?

Again, please understand I don't know much about the topic.

 

[Vanadium 50]

Above a few 10's of GeV, you need the full electroweak theory (of which QED is a low-energy approximation) to do calculations. So, no, it is not complete.

 

[Parlyne]

I think that the fairest statement here is that QED can be seen as either complete or correct, but not both. QED, taken by itself, is a perfectly self-consistent theory of electromagnetic interactions. However, the fact that it only includes electromagnetic interactions means that it is not a correct description of how electromagnetism works in the world. Even at low energy, it is possible to make electromagnetic measurements sufficiently precise that small quantum corrections due to the strong and weak forces (which are, of course, not included in QED) are evident. And, as Vanadium pointed out, at high energy, failure to use the full electroweak theory will guarantee that your QED predictions are very wrong.

 

[DrDu]

Also take in mind that QED is basically a set of rules of how to calculate terms in a divergent perturbation series. Therefore mathematicians refuse to call QED a theory at all.

 

[Vanadium 50]

Actually, pure QED has a problem, called the Landau pole. At sufficiently energetic scales, the QED predictions become nonsensical. However, this scale is far, far, far above the point where you need to go to the full electroweak scale, so this problem is somewhat academic.

 

[nlsherrill]

So how come it seems I always see people doing research in QCD not QED? I also thought that electromagnetism and the weak force were already unified(or maybe just mathematically described together)?

what i am getting from this is that you need different theories at different energy levels? So if this is true, at low enough energy classical electromagnetism is a good approximation, and at some higher energy level you need QED, then even higher energy electroweak?

 

[IRobot]

So how come it seems I always see people doing research in QCD not QED? I also thought that electromagnetism and the weak force were already unified(or maybe just mathematically described together)?

what i am getting from this is that you need different theories at different energy levels? So if this is true, at low enough energy classical electromagnetism is a good approximation, and at some higher energy level you need QED, then even higher energy electroweak?

Well as long as we don't have a theory of everything, if it exists, theories have always their domain of applicability (low speed compared to c, not quantum, weak gravitational field, ...).

 

[Parlyne]

So how come it seems I always see people doing research in QCD not QED? I also thought that electromagnetism and the weak force were already unified(or maybe just mathematically described together)?

what i am getting from this is that you need different theories at different energy levels? So if this is true, at low enough energy classical electromagnetism is a good approximation, and at some higher energy level you need QED, then even higher energy electroweak?

QCD is the theory of the strong force, not the weak force; and, there' so much research into QCD because it's extraordinarily hard to make predictions correctly from QCD. The methods that we use to make extremely precise predictions from QED (or the electroweak theory as a whole) only work for QCD at very high energy. Unfortunately, the most interesting systems involving QCD are actually at low energy. And, even worse, QCD at all energies contributes corrections to electroweak processes to the extent that the biggest uncertainties in the predictions for the most precisely measured electromagnetic quantities tend to come from the QCD corrections.

As for classical electromagnetism, it tends to work best for reasonably large systems at low(ish) energy.

 

[nlsherrill]

Thank you all for the responses.