# Looking for book on Introduction to QFT

1. Nov 27, 2012

### ods15

Hi. I'm studying (introduction to) QFT, and I'm really lost. If possible, I'd like a pointer to a good textbook on the subject. I'll give an example of my confusion with a question:

I think I've understood phi(x) as a classical scalar field, what it is and how to use it in a lagngian for classical field theory.

I'm totally lost on how it works in QFT. My understanding is that it is now an operator on the hilbert space of states, like X or P were in quantum mechanics. Actually, it is a whole group of operators - each phi(x) give a different operator for a different x

In quantum mechanics, the way the X operator worked, it was an observable, with eigenvectors being definite states and eigen values being the values of the observable....
What's going on with phi(x)? What is this operator? Why am I using it like I used the classical scalar field phi(x)?​

Before even getting into any of the ugly calculations and normalizations, I'm trying to understand the basic "rules and players". What are the different operators and functions, what do they depend on, what do their values means, how are they dynamical...

I'm very mathematically minded, so I'm hoping to find a book in that style. As an example - I really like Sean Carroll's General Relativity textbook.

2. Nov 27, 2012

### RUTA

Quantum Field Theory in a Nutshell, A. Zee, Princeton Univ Press, 2003 (although, I believe there is a newer edition).

3. Nov 27, 2012

### ods15

I actually skimmed it already and I thought it didn't go into detail much of definitions and how to go from classical field to quantum field, but maybe I didn't give it enough of a chance, I'll try it now, look more carefully, since it's such a short book anyway. Thanks!

4. Nov 27, 2012

### tom.stoer

5. Nov 27, 2012

### RUTA

6. Nov 27, 2012

### Sonderval

If you are mathematically minded, grab hold of Hatfield "QFT of point particles and strings" (I feel like an echo chamber sometimes, always recommending this.) It nicely explains the basics in three different ways. Srednicki is also quite nice. Many people don't like it, but I would also recommend to have a look at Bob Klaubers qftfieldtheory-info site - he has an idiosyncratic take on many concepts (like vacuum fluctuations, where I am sure he is wrong...), but he explains the basics in a very didactic (and mathematical) way and he always states clearly when what he writes is not the standard interpretation.

Your confusion with the meaning of phi is possibly due to the fact that "What is phi in QFT" has two completely different answers:
In path integral formulation, phi is a classical field that has a value at each spacetime point. The path integral accounts for the quantum-mechanical superposition of different possible field values.
In canonical formulation, the phi's become operators because at least in principle, the classical phi(x) is an observable. The trouble (at least to my understanding for a long time) is that these operators of course have to act on quantum state vectors - usually the vacuum state; and almost nobody tells you what that is (Hatfield does in detail, Srednicki has an exercise on it, but without a solution that may not help you much and be frustrating).
I wrote a bit on that in this thread:

7. Nov 27, 2012

### cosmic dust

I strongly recomment you to study Weinberg's book "The Quantum Theory of Fields, vol 1 - Foundations" . It requires some knowledge of group theory to get start and a good understanding of general QM formalism. You will see that quantum fields are a direct consequence of the CORRECT merging of QM and SR. In my opinion, the second quantization approach (wich involves fields turning to operators- this is not the case of this book) is just a makeshift (like Dirac sea) in order to solve the paradoxes that appear when someone does relativistic wave-meachanics. Try Weinberg's method (if it is not too hard for you) and your confusion will probably disappear.

8. Nov 28, 2012

### Sonderval

Shows how tastes differ - I hate the Weinberg-book because to me it seems never to get to the actual physical interpretation of the equations.
Probably the best idea is to read the first two chapters or so of several QFT-books and see which ones you like best.

9. Nov 28, 2012

### haushofer

Weinberg is nice if you already know the subject and want to deepen your understanding. For an introduction I think it's absolutely not the right book to start with. The same goes for Zee's book: that has some really nice things in it, but for an introduction it's not good, mainly because of the lack of rigour and computations. If you know the subject already a bit it's a very nice book to read, because it gives clarifications and insights which are not (or hard) to be found elsewhere.

I would recommend Ryder or Srednicki. I also found Peskin&Schroeder nice (that's the book I really used as my first introduction), they stress the second quantization and only at half the book introduce path integrals. It has a lot of computational details in it, but also give nice conceptual explanations.

10. Nov 28, 2012

### HomogenousCow

Glad to see I am not alone, I started the thread suggested above and am still very very confused.
I too, have no idea what the "rules and players" are.
It would be very helpful if someone gave us a direct list of posulates like the case in Shankar's principle of quantum mechanics.
For example do the X and P operators for particle states still apply?
How do I solve the basic problem of physcs, If I leave some multiparticle in A state, what happens to it some time T after in my frame??

11. Nov 28, 2012

### ods15

Thanks for the replies everyone!

HomogenousCow, I'm also glad to see I'm not the only one with these questions, your confusion seems very similar to mine. Interesting timing we had...

I've been recommended a few things by a few people, so here's my summary, in order of recommendation:

Lectures Notes:
0) http://isites.harvard.edu/fs/docs/icb.topic1088741.files/Quantum-Theory_Relativity.pdf (background)
1) http://arxiv.org/pdf/1110.5013v4 - Lecture notes by Sidney Coleman, recognized by some as the best available
2) http://isites.harvard.edu/icb/icb.do?keyword=k87741&pageid=icb.page507113
3) http://www.physics.utoronto.ca/~luke/PHY2403/References_files/lecturenotes.pdf

Books:
1. Srednicki (free pdf, can email for solutions)
2. Zee (nutshell)
3. Peskin & Schroeder
4. Weinberg - The Quantum Theory Of Fields Vol 1 Foundations

A more mathematical book - Brian F. Hatfield - Quantum Field Theory Of Point Particles And Strings
Somewhat non-standard book - Robert D. Klauber - http://www.quantumfieldtheory.info/
Another book - Lewis H. Ryder - Quantum Field Theory
Postulates for relativistic QFT are in section 3.5 of http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4282179/non11.pdf

So right now, my plan is to read (0) and (1), with filling in holes from 1. I haven't started yet, I'll report back how it goes...

Last edited: Nov 28, 2012
12. Nov 28, 2012

### HomogenousCow

I'm looking for a book like shankars treatment of QM, starting from he vey bare bone structure to advanced stuff

13. Nov 28, 2012

### Sonderval

"For example do the X and P operators for particle states still apply?"
Not really.
Since you want to be relativistic, you have to treat t and x on the same footing. In QM, t is a "label", x is an operator. In QFT, you would either have to make the time an operator (difficult), or consider t and x as a label of a field.
Then you have two possibilities: Either you use the path integral and treat the field as a classical field, or you promote the field to an operator acting on states.

@ods
You mght also try Michael stones "The physics of quantum fields", that's also well-written.

14. Nov 28, 2012

### Lapidus

Do yourself a favor and read David Tong's lecture notes as a starting point. If you get lost in Srednicki, read Matthew Robinson's "Symmetry and the Standard Model".

Last edited by a moderator: May 6, 2017
15. Jun 18, 2013

### omephy

Srednicki's book is very frustrating for a beginner who is studying it without any teachers help. Peskin or Ryder is good for starting QFT. Srednicki uses $$\phi^3$$ theory and there are no additional resources available on the net compatible with this book. You may find some class notes/slides which are not very helpful.