Should QFT Be Taught from First Principles Like Weinberg?

[Hyperreality]

Looking at most textbooks, I found Weinberg's Quantum Theory of Fields to be by far the most superior and I think that's how QFT should be taught as well.

I also think the way Weinberg presenting the subject from first principle is the way to make progress in research in fields such as quantum gravity.

Recently reading his classic paper on Feynman Rule for Any Spin, I have come to admire his clear vision and ability to create a formalism for a difficult subject like quantum field theory.

Unfortunately that doesn't seem to be how quantum field theory is taught in most graduate classes! We really should teach the subject from first principle like we do for special and general relativity.

I just like to hear people's opinion on how QFT courses is taught in most places and should be taught.

 

[meopemuk]

HyperReality,

I totally agree. Weinberg's approach to QFT is the only one which makes sense to me. I spent many years reading various QFT textbooks and not getting it until I stumbled upon Weinberg's writings in 1960's and later on his textbook. I also attempted to write my own textbook, which follows Weinberg's footsteps http://www.arxiv.org/abs/physics/0504062


Eugene.

 

[Dr Transport]

Two books come to mind: Mandel and Shaw, Aitcheson and Hey were both used when I was in grad school in the late '80's early '90's. Both were readable and if I pick them up today, I can still get thru them.

Feynman's is also very good, and from the master first principles.

 

[malawi_glenn]

Here we have a 17.5 credits course called 'Relativistic Quantum Mechanics and Quantum Field Theory'

The first half one uses the first part of the book: 'Relativistic Quantum mechanics and field theory' by Gross, and the second part 'QFT' by Peskin..

But is more than what book you use, the exercises you do, the extra material, the topics etc.

 

[Fredrik]

I found Weinberg's Quantum Theory of Fields to be by far the most superior and I think that's how QFT should be taught as well.

Weinberg's approach to QFT is the only one which makes sense to me.

This is how I feel too. However, if you're going to teach an introductory QFT class to a group of people that includes experimentalists, it probably makes more sense to use some other book. An introductory class based on Weinberg would probably be at least twice as long as one based on Mandl & Shaw, and much more difficult for the students.

I know that the "traditional" presentation is kind of weird, and doesn't really make sense until you've studied a few chapters of Weinberg. Students won't even understand the "particle" concept very well until they've studied Weinberg's chapter 2. But experimentalists don't care about that stuff anyway. I think they wouldn't like an introductory class based on Weinberg's book.

That stuff is important very important though. I would feel uncomfortable if I had to teach a class that doesn't cover those things. I think a good idea for an introductory class is to use an "easy" book like Mandl & Shaw, and also teach Weinbergs chapter 2, which explains the particle concept and the whole point of the canonical quantization procedure (to construct representations of the Poincaré group).

My university (Stockholm) handled this stuff very badly (in the late nineties). First we had a 5-week class (it took 10 weeks because we had another 5-week class at the same time) called "relativistic quantum mechanics" which taught canonical quantization of field theories without interaction terms and some stuff from Sakurai's "Advanced quantum mechanics". Next year we had a 10-week class based on Mandl & Shaw called "quantum field theory", and the year after that a 10-week class based on Peskin & Shroeder called "quantum field theory 2" which taught almost exactly the same things we had already studied using Mandl & Shaw. The end result was a bunch of people who had studied quantum field theory for 25 weeks and pretty much only understood canonical quantization of the simplest theories (QED being the most complicated one), a little about how to use the Feynman rules, and almost nothing about renormalization and other advanced topics. We knew nothing about the relevance of group representations.

(I think Mandl & Shaw is a pretty good book if you just want an easy introduction, but that's not the reason I keep mentioning it. It's just the book I'm most familiar with. There may be lots of better books out there).

 

[malawi_glenn]

We have approx the same outline in Uppsala, but in our grad-course QFT2, we learn renormilazation, SSB, QCD etc. Feynman rules are included in our first part of the 2part course 'relativistic quantum mech.'

 

[Fredrik]

We have approx the same outline in Uppsala, but in our grad-course QFT2, we learn renormilazation, SSB, QCD etc. Feynman rules are included in our first part of the 2part course 'relativistic quantum mech.'

I didn't mean to imply that we weren't taught renormalization at all. We just didn't learn it. The same goes for spontaneous symmetry breaking. (The books probably explained these things reasonably well, and the teacher at least explained some of it in both classes, but we didn't have to know anything about it to pass). We weren't taught anything at all about QCD though. That was a different class (which I didn't take).

 

[malawi_glenn]

I didn't mean to imply that we weren't taught renormalization at all. We just didn't learn it. (The books probably explained it reasonably well, and the teacher at least explained some of it in both classes, but we didn't have to know anything about it to pass).

aha, I see. But you used Sakurai, Mandl & Peskin in stockholm? You had the same teacher in all three classes?

 

[Fredrik]

aha, I see. But you used Sakurai, Mandl & Peskin in stockholm? You had the same teacher in all three classes?

We had Lars Bergström for the Sakurai class, and Ulf Lindström for the other two.

 

[malawi_glenn]

Same Ulf Lindström as we have here in Uppsala ;-)

http://en.wikipedia.org/wiki/Ulf_Lindstrom

 

[Hyperreality]

HyperReality,
I also attempted to write my own textbook, which follows Weinberg's footsteps http://www.arxiv.org/abs/physics/0504062
Eugene.

Thanks meopemuk, this looks like a very nice book!

But is more than what book you use, the exercises you do, the extra material, the topics etc.

This is true. But I also think having a good book is like having a good teacher. Their style of teaching and ways of conducting research strongly influences the students. This is something you don't learn by doing exercises and solving problems.

This is how I feel too. However, if you're going to teach an introductory QFT class to a group of people that includes experimentalists, it probably makes more sense to use some other book. An introductory class based on Weinberg would probably be at least twice as long as one based on Mandl & Shaw, and much more difficult for the students.

Yes you are absolutely right the book is probably suitable only for theorists and students with good backgrounds.

Reading and understanding Weinberg is not an easy task, but it is totally worth it. At first sight, it may look daunting, but once you get into it, I think you will find it to be very well-written and the notations he uses are not that intimidating.