Peskin & Schroeder: Opening p.20 to Understand Equation 2.21

[Ratzinger]

would someone mind opening his/her beloved P&S and help me out..

on p.20 it says if we expand the classical Klein-Gordon field in Fourier (momentum) space, we arrive at equation 2.21...why is that?

gracias

 

[Hans de Vries]

would someone mind opening his/her beloved P&S and help me out..

on p.20 it says if we expand the classical Klein-Gordon field in Fourier (momentum) space, we arrive at equation 2.21...why is that?

gracias

Remember that taken the n'th derivative becomes multiplying by pⁿ in
the Fourier domain? So taking the second order derivatives:

$$\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2}$$ becomes multiplying by: $$p_x^2 + p_y^2 + p_z^2$$ in the Fourier domain.


Regards, Hans.

 

[Ratzinger]

yes, of course... thanks Hans

But when I read on I keep sratching my head over how they get from one equation to the next. It's not too hard, but I always miss some little information.

What then makes me wonder why it's impossible for the physics community to write an understandable but honest QFT text for undergraduates, researchers from other fields or the motivated laymen. There are such books for QM and GR, now I heard even for string theory. Although there are thousands of QFT texts, I found not one truly pedagogical and introductory.

Or is QFT simply so hard and impenetrable, does it require simply many years of 'doing physics' and the intuition and skills that come along with it?

 

[Hans de Vries]

yes, of course... thanks Hans

But when I read on I keep sratching my head over how they get from one equation to the next. It's not too hard, but I always miss some little information.

What then makes me wonder why it's impossible for the physics community to write an understandable but honest QFT text for undergraduates, researchers from other fields or the motivated laymen. There are such books for QM and GR, now I heard even for string theory. Although there are thousands of QFT texts, I found not one truly pedagogical and introductory.

Or is QFT simply so hard and impenetrable, does it require simply many years of 'doing physics' and the intuition and skills that come along with it?

The (by far?) best pedagogical text for QFT for me is Lywis H. Ryder's book
"Quantum Field Theory" I do highly recommend it.



For self study it's better then both Peskin & Schroeder and Zee. It's also more
modern in the sense that it introduces Wigner's 1939 work on the Poincare
group while deriving Dirac's equation. You won't find anything about this
in P&S or Zee, leaving you wondering what all this spinor stuff means.

Steven Weinberg follows the modern approach with the Poincare group also
in his three volume set "Quantum Theory of Fields, I, II and III", but it's
much more formal.




Regards, Hans

 

[selfAdjoint]

I have always thought there should be a course on QFT tricks of the trade, manipulating integrals, delta functions, transforms, doing the surface term trick, and what have you. Nothing but excercises, excercises, excercises, until it's second nature.

 

[fliptomato]

Peskin and Schroeder is the gold standard for learning how to do quantum field theory (i.e. how to do calculations), though it takes a little more foresight with the book to actually understand QFT.

While this "ground zero" calculational approach is an important (perhaps prerequisite) of QFT pedagogy, I suggest supplementing Peskin and Schroeder with Zee's , which addresses actual understanding. Zee is very light on calculations (making it a much easier read) and teaches how to interpret QFT. It's a little difficult to read Zee and Peskin concurrently, since Zee goes straight to the path integral formalism while Peskin doesn't introduce that until Part II of his book, but I found it helpful to read particular sections of Zee as I went through Peskin and then re-read Zee straight through after finishing all of Peskin.

As far as physics books go, Zee's actually a lot of fun to read, as well.

 

[tavi_boada]

It's a little difficult to read Zee and Peskin concurrently, since Zee goes straight to the path integral formalism while Peskin doesn't introduce that until Part II of his book

You're right, it is difficult.

how can someone who has trouble with quantizing the Dirac field (like most of us at first), go directly to and understand ghosts in the path integral quantization? The only problem with Peskin, in my opinion, is that it leaves too many calculations to the reader. As someone said, "devil is in details" and you must work them out to understand anything.

 

[selfAdjoint]

I think the idea with Zee is that you are not supposed to be really interested in working out the expressions in the test. It was intended for physicists who needed a little field theory but did not intend to become field theorists. There are other boooks that take you by the hand with the Dirac field, an old one like Ryder, for example.

 

[fliptomato]

I agree with both Tavi and selfAdjoint. At a first read, it's difficult to pick up ghosts and supersymmetry, and lots of the things in QFT. However, I do believe that Zee's path integral presentation is the most physically-grounded introduction to QFT. Will you pick up all the nuances? Probably not. But you will get an honest, grounded big-picture for the subject, which helps guide you through the calculations in Peskin.

Personally, I found it difficult to keep up with all the moving parts of Peskins presentation of the path integral formalism, and it took a couple of reads to get it right. After going through most of Peskin, I read Zee, and discovered that many of the tangible things that I was missing was presented directly in Zee. Of course, if you read Zee first, it can be hard to feel like you're doing anything concretely since you're not "anchored" to line-by-line calculations, but this is why both approaches should be used to support one another.