# Peskin, Schroeder

## Main Question or Discussion Point

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

## Answers and Replies

Related Quantum Physics News on Phys.org
Hans de Vries
Gold Member
Ratzinger said:
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.

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
Gold Member
Ratzinger said:
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.

https://www.amazon.com/exec/obidos/ASIN/0521478146/qid=1124050639/sr=2-1/ref=pd_bbs_b_2_1/103-2960849-2823825

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.

https://www.amazon.com/exec/obidos/tg/detail/-/0521550017/qid=1124051330/sr=1-1/ref=sr_1_1/103-2960849-2823825?v=glance&s=books

Regards, Hans

Last edited by a moderator:
Staff Emeritus
Gold Member
Dearly Missed
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.

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 https://www.amazon.com/exec/obidos/tg/detail/-/0691010196/qid=1124054583/sr=8-1/ref=pd_bbs_1/102-2727065-8958565?v=glance&s=books&n=507846, 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.

Last edited by a moderator:
fliptomato said:
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.

Last edited: