Good introductions to quantum field theory and vacuum

[Sojourner01]

I am to produce a research presentation for a class of Masters' physics students on the casimir force, going via a detailed treatment of the vacuum effects in conducting cavities, going on to explain some real phenomena and applications. What I am after is a good introductory text on quantum fields, in particular vacuum fluctuations. Most that I have been able to find are texts that deal more with particle physics rather than 'no-particle physics' that I'm looking for, with the exception of one - Cavity Quantum Electrodynamics by Paul Berman which is interesting but very specialised in its examples, and doesn't give an accessible treatment of the basic effects. I'd also like to understand more about the difference between the virtual particle and vacuum expectation value approaches, and whether they are merely philosophical in nature or whether they have significant differences in derivation.

I'm intentionally posting this here since although it's technically a homework assignment, I'm not asking for help with answers.

 

[George Jones]

I am to produce a research presentation for a class of Masters' physics students on the casimir force, going via a detailed treatment of the vacuum effects in conducting cavities, going on to explain some real phenomena and applications. What I am after is a good introductory text on quantum fields, in particular vacuum fluctuations. Most that I have been able to find are texts that deal more with particle physics rather than 'no-particle physics' that I'm looking for, with the exception of one - Cavity Quantum Electrodynamics by Paul Berman which is interesting but very specialised in its examples, and doesn't give an accessible treatment of the basic effects. I'd also like to understand more about the difference between the virtual particle and vacuum expectation value approaches, and whether they are merely philosophical in nature or whether they have significant differences in derivation.

I'm intentionally posting this here since although it's technically a homework assignment, I'm not asking for help with answers.

I think you are more likely to get results here than in a homework forum.

Aitchison has a long pedagogical article, "Nothing's plenty: The vacuum in modern quantum field theory," in Contemporary Physics, 26(4), 1985.

I have been meaning to read this article for quite some time, but I yet to to get around to doing so, so I don't know if it will be of any help to you.

 

[Count Iblis]

http://arxiv.org/abs/hep-th/0503158"

 

[blechman]

Before I saw your link, Count Iblis, I was going to suggest that you check out any review articles by Bob Jaffe. He's one of the leading experts of the field. Then I saw your "interesting article"!

That probably is the best place to begin (and the references he points to). There's a book by Applequist and Chodos and Freund called "Modern Kaluza-Klein Theories," which is a collection of original papers on extra dimensions. there's a whole section on Casimir, including Casimir's original conference proceeding - I've never seen it anywhere else.

Have fun!

 

[Sojourner01]

Interesting, Count, but from my point of view largely incomprehensible. I can gather that - more or less - Jaffe is suggesting that the invocation of zero point fluctuations is unnecessary for deriving the Casimir effect, but very little else. He uses a great deal of terminology and mathematical formalism that it's unreasonable to expect an undergrad to be familiar with.

 

[Count Iblis]

Interesting, Count, but from my point of view largely incomprehensible. I can gather that - more or less - Jaffe is suggesting that the invocation of zero point fluctuations is unnecessary for deriving the Casimir effect, but very little else. He uses a great deal of terminology and mathematical formalism that it's unreasonable to expect an undergrad to be familiar with.

You'll encounter that very often if you get into physics research. By the time you've mastered all of this formalism you'll read articles on more advanced topics and may agaiun encounter a similar problem.

Often you can read the article without understanding most of the formalism. Not always, but in this case you did understand what the article is saying. The formalism is just gives you some information on how to compute the Casimir effect from first principles (without using the heuristic argument involving the shift in zero point energies).

The article says that the Casimir effect is just like a van der Waals force between neutral objects. A fully fledged derivation is given in the book "Quantum Field Theory" by Itzykson and Zuber in section 7-3-3 on page 365.

 

[Sojourner01]

Thanks for the article. Actually, one of his references (11 I think) is much more clear and on my level and goes through the whys and wherefores, including regularisation techniques.

 

[Sojourner01]

Sorry to dig up such an old thread, but I feel I have to pry for a few more answers. You see, the event in question is tomorrow and I am far from ready for all the off-the-wall questions that are bound to arise.

So; what is Bob Jaffe's point? That a QED approach that specifies the interaction entirely in terms of the properties of the plates is sufficient, and that the vacuum in between is inconsequential? Can the two approaches be equivalent under any current theoretical framework? If not, the implications are somewhat troubling. Since I know little if any QED, I'm not sure I can make an educated judgement.

What I'm more worried about is that my explanation may be a bit cross-eyed. Bearing in mind that this is for a mixed undergrad-level audience and thus is probably quite banal, I've said:

Quantum uncertainty is a property of space (or technically the fields that occupy all space) and not uniquely of particles

If particles can perform one-loop interactions under the uncertainty principle, so can no-particles. The common example of this is the Dirac electron-positron system responsible for vacuum polarisation

The electromagnetic field fluctuations yield a continuum of virtual photons across the bounded region. Their probability distributions are cumulative and thus constructive interference over all space forces only integer-wave bulk fluctuations to exist within the bounded region, since at the bounds the electric and magnetic field amplitudes have to be zero.

Is this correct, aside from floppy use of terminology on my part? Or am I mixing my metaphors and including bits of the QED approach by mistake, since that's what it sounds like given further reading?