Exploring Quantum Field Theory: A Student's Perspective

[da_willem]

At my physics faculty there is this magazine that comes out once every three months. I wrote an article about GR for it. Introducing not only the concepts but also some mathematics. I explained the field equations and derived some implications of the Schwarzschild metric. I could do this because I read some books about it in the summer.

Now I'm supposed to write a similar piece, so with mathematical backup, about QFT. But as a third year (applied-)physics student I have not encountered the subject in class. And I actually found the books I opened about it quite intimidating.

I will try to read a book about it, because what I've seen about it it seems like a very interesting subject. But I would like to know if (you think) it is possible to give a comprehensive outline of the ideas not only in words to an audience of physics students from sophomores to graduates. Not everybody has to understand everything. But I would like those who had an introductory course in QM, SR, and have seen the EL en Hamiltonian formalism to grasp the ideas; including myself! And I would like to show some of the good stuff from QFT, to enthousiasm the readers.

I would also like to know what aspects of the theory are not too difficult and interesting. Like is it very difficult to derive the Casimir force between two parallel plates? I already found out deriving the KG equation is easy and the Dirac equation is also doable. So I would like to start with that. But what other subjects are interesting and can be explained in an article of let's say 3000 words?

And are there any good sites about QFT. I already found Wikipedia had a lot of interesting articles.

 

[da_willem]

Can anybody enlighten me?

 

[ZapperZ]

Since no one has responded, and you sounded so desperate in your plea (hehehehe), I'll throw out a few links here for you. I have no idea if these are what you want, or if they'll even be of any help...

http://xxx.lanl.gov/abs/hep-th/9803075 <-- this is by Frank Wilczek, our 2004 Nobel prize winner.

http://xxx.lanl.gov/abs/hep-ph/0010035

http://arxiv.org/abs/math-ph/0204014

If I were you, I'd narrow down the range of coverage of QFT, and look at how it is used in many-body physics (see, for example, http://www.physics.ucla.edu/~nayak/many_body.pdf ). This has crucial applications in condensed matter physics. The audience needs to be told that these apparently esoteric methodology has applications in the very devices they use everyday.

Zz.

 

[da_willem]

Thanks, I did sound kinda desperate... Could you explain what kind of applications QFT has, so to save me to read a 338p book on which I haven't even had an introductory course (next period I get solid state physics...)?

 

[ZapperZ]

Thanks, I did sound kinda desperate... Could you explain what kind of applications QFT has, so to save me to read a 338p book on which I haven't even had an introductory course (next period I get solid state physics...)?

I'll just give you one quick example of QFT in condensed matter - the derivation of BCS theory of superconductivity.

.. and I'm not even scratching the surface by saying that. There are tons more.

Zz.

 

[da_willem]

And do you think any of these examples can be worked out without having studied all of QFT, or have your MSc in mathematics or physics? I just found out it isn't too difficult to derive the Casimir force, at least in one dimension, from the principles that follow from QFT.

 

[ZapperZ]

And do you think any of these examples can be worked out without having studied all of QFT, or have your MSc in mathematics or physics? I just found out it isn't too difficult to derive the Casimir force, at least in one dimension, from the principles that follow from QFT.

I wouldn't know.

You can derive the BCS theory without using QFT, such as using variational technique. But it is way more elegant and a lot more transparent using field theoretic methods, since you start right away with the coupling mechanism that forms the cooper pairs.

Zz.