What Are the Key Concepts of Quantum Field Theory?

[bhobba]

I found some excellent videos from Berkeley on what QFT is.
https://www.youtube.com/@hitoshimurayama2746

The view is that QFT is simply a multi-particle ordinary QM. The videos give the full details, so I won't say anything else except to mention some highlights. Particle creation, Compton scattering, and a number of other things simply can't be explained by QM, but QFT can explain them.

Here's a thought to ponder - does QFT resolve fundamental things like wave-particle duality and the measurement problem?

Thanks
Bill

 

[PeterDonis]

The view is that QFT is simply a multi-particle ordinary QM.

This doesn't really make sense since QFT is a quantum theory of fields, not particles (hence the name).

The videos give the full details

Are there any papers referenced? I am, to put it mildly, not a fan of this apparent trend of using videos for this purpose. I can read the relevant material in a textbook or paper much, much, much, much faster than it can possibly be communicated in a video.

does QFT resolve fundamental things like wave-particle duality

Wave-particle duality isn't a "fundamental thing", it's a pop science misconception.

and the measurement problem?

No.

 

[Nugatory]

Here's a thought to ponder - does QFT resolve fundamental things like wave-particle duality and the measurement problem?

No, which is why you are justified in saying "simply a multi particle ordinary QM", where "simply" can be read as "no more than" and "ordinary" as "doesn't do anything extraordinary (like resolving the measurement problem)".
"Important" is a different question with an obvious answer.

 

[PeterDonis]

a multi-particle ordinary QM

In the notes for Hitoshi Murayama's QFT course at Berkeley [1], there is the following interesting statement (Section 1.2):

"the contents of multi-body quantum mechanics and quantum field theory are exactly the same in systems where the number of particles does not change"

Note the key qualifier at the end of that sentence. With that qualifier, the statement is true, but the whole point of QFT, as you can gather from the notes, is that QFT, unlike multi-body QM, can be applied to systems where the number of particles does change. So it is not correct to say that "QFT is simply a multi-particle ordinary QM".

[1] http://hitoshi.berkeley.edu/221B/QFT.pdf

 

[bhobba]

http://hitoshi.berkeley.edu/221B/QFT.pdf

Thanks for posting that, Peter, much appreciated.

I should have posted the paper to meet our guidelines.

You are correct about wave-particle duality—Dirac's transformation theory definitely eliminated it in 1926, if not before.

Interestingly, the notes you posted also use the concept

Thanks
Bill

 

[PeterDonis]

the notes you posted also use the concept

Kinda sorta. They use the term "wave-particle duality", but only in the course of making an observation about how ordinary QM and QFT start from opposite classical descriptions but end up with a quantum model that has aspects of both.

 

[pines-demon]

The view is that QFT is simply a multi-particle ordinary QM.

This is kind of true, I mean at least originally. In condensed-matter theory studying many-body theory is usually the equivalent of studying non-relativistic quantum field theory. I think historically QFT is born out of trying to quantize the EM field but also from trying to treat $N$-body problems.

Particle creation, Compton scattering, and a number of other things simply can't be explained by QM, but QFT can explain them.

Compton scattering was explained by Compton without the need of QFT. Particle creation cannot be included in non-relativistic QM, but if we are talking about simply admitting that there are anti-particles, then non-field theory can deal with that, it is just more ad-hoc. I do not think these are good examples of non-field QM.

Here's a thought to ponder - does QFT resolve fundamental things like wave-particle duality

Indeed, there is no wave or particle, there are just fields.

and the measurement problem?

Nope, it does not even try. Edit: the notes do not seem to do that either.

 

[Vanadium 50]

I would hope that if the Mentors are recommending a multi-hour set of videos. at least a few of them will have watched them checking for correctness and clarity. Berkeley is a fine school, but it it is hard to say they have never had a confusing lecture.

Without wading through the hours of video, I disagree with the statementL

QFT is simply a multi-particle ordinary QM.

I very much doubt Hitoshi said this, at least not in context. There are two differences: QFT is relativistic, and you are not necessarily in an eigenstate of the number operator.

More generally, I don't think replacing months of guided study with a sound bite is effective or helpful. QFT is neither simple nor trivial.

 

[bhobba]

Point taken.

I am the only mentor involved in posting them. I watched the first three and thought the perspective was different in a good way.

However, as it has become clear, what I got from them is likely not what was intended.

Thanks
Bill

 

[A. Neumaier]

QFT is relativistic, and you are not necessarily in an eigenstate of the number operator.

Even worse, for interacting relativistic QFTs there is no number operator. Particles are meaningful only in asymptotic states (i.e., as input and output states of scattering experiments), where the fields interact only minimally, hence can be treated as essentially free.