Discover the Best Lightweight QFT Introductions for Self-Study

[compsciconvert]

I was a denizen of this forum some 15 years ago during undergrad. However I since joined the dark side working in software on ML, AI, and distributed data processing.

Every now and then I pick up a physics textbook to get into the weeds of a topic I would have missed due to skipping out on grad school. I'd like for QFT to be the next topic I tackle in this manner but unfortunately I haven't had much luck finding the right resource.

Is there a good list of lightweight QFT introductions that folks have found beneficial? I'm mainly looking to familiarize myself with the theory enough to understand the mathematics in detail along with core research problems in the field - but I will probably only take on a practice problem or two at most.

 

[Vanadium 50]

What is your background? Especially in QM and math methods.

 

[compsciconvert]

I've done 2 grad semesters of QM and 2 grad semesters of Mechanics. I've kept my math reasonably up to date due to my job. My contour integration is weak, but my differential geometry, linear algebra, and PDE skills are still fairly sharp.

 

[physicsworks]

If QM and basic relativity are no problem, I would recommend Maggiore's A Modern Introduction to Quantum Field Theory. It provides a thorough introduction, has many worked out examples and (!) solutions to problems after each chapter in the back.

 

[PeroK]

I've done 2 grad semesters of QM and 2 grad semesters of Mechanics. I've kept my math reasonably up to date due to my job. My contour integration is weak, but my differential geometry, linear algebra, and PDE skills are still fairly sharp.

There's also "QFT for the Gifted Amateur" by Lancaster and Blundell. Assuming you are sufficiently gifted.

 

[malawi_glenn]

Srednicki is king!

 

[apostolosdt]

Your QFT textbooks you can profitably choose depend on your physics/math background.

Mechanics: You should revise (if needed) Lagrangian and Hamiltonian stuff. No in-depth details, but you should eventually feel very comfortable with quick calculations. Level similar to Goldstein's Chapter 12 (2nd ed.).

Mathematics: Contour integration, Hilbert spaces, Fourier transforms, and groups are all "must" topics. You can't finish a single page without being sufficiently good at them.

Provided that your special relativity and quantum mechanics background is good, I think you can start with any standard textbook on QFT. More math will be presented to you as you're reading your book.

One final piece of advice: Start with canonical commutators rather than path integrals for field quantization; the latter is modern and powerful, but the former better syncs with QM.

Both Maggiore and Srednicki mentioned by others are very good textbooks.

 

[The Bill]

Mathematics: Contour integration, Hilbert spaces, Fourier transforms, and groups are all "must" topics. You can't finish a single page without being sufficiently good at them.

How much explicit training in group theory do most physics graduate students have before their first QFT course? Is it taught in most undergraduate programs nowadays?

From talking to my undergraduate physics major friends when I was in university about 20 years ago: Most of them had heard group theory mentioned as something "they'd see later" in connection with symmetry, but were never exposed to the group axioms, representation theory, or anything beyond a little handwaving about symmetry. That's during their entire undergraduate educations for physics bachelor of science. This is a small sample size in both people and universities, from about a half-decade period 20 years ago, so /shrug.

None of my personal friends went on to PhD programs in physics, so I don't have any secondhand experience with those programs back then.

I'm just curious about the current expectations. Maybe a little group theory is nearly always taught in undergraduate math methods now?

 

[vanhees71]

How much explicit training in group theory do most physics graduate students have before their first QFT course? Is it taught in most undergraduate programs nowadays?

It's always too little. If you really want to understand the details of "why relativistic QFT looks the way it looks" you have to self-study this important topic. A very good book for this is

R. U. Sexl and H. K. Urbantke, Relativity, Groups, Particles, Springer, Wien (2001).

From talking to my undergraduate physics major friends when I was in university about 20 years ago: Most of them had heard group theory mentioned as something "they'd see later" in connection with symmetry, but were never exposed to the group axioms, representation theory, or anything beyond a little handwaving about symmetry. That's during their entire undergraduate educations for physics bachelor of science. This is a small sample size in both people and universities, from about a half-decade period 20 years ago, so /shrug.

Usually nowadays most professors teach Noether's theorem in the analytical-mechanics lecture at least, but as I said usually group theory is not well covered in the standard course lectures.

None of my personal friends went on to PhD programs in physics, so I don't have any secondhand experience with those programs back then.

I'm just curious about the current expectations. Maybe a little group theory is nearly always taught in undergraduate math methods now?

That would indeed by highly desirable but unfortunately it's usually not done in the standard math curriculum for physicists either :-(.

 

[apostolosdt]

How much explicit training in group theory do most physics graduate students have before their first QFT course? Is it taught in most undergraduate programs nowadays? [...] Maybe a little group theory is nearly always taught in undergraduate math methods now?

I can't disagree with these comments. I assumed that compsciconvert, having said that he had completed two semesters in QM and two in Mechanics, both at the graduate level, had been exposed to some basic topics in symmetries and groups.

Groups and intro to representation theory are sometimes taught during senior year as topics in math methods in physics classes, at least in European universities offering four- or five-year curricula.

 

[apostolosdt]

R. U. Sexl and H. K. Urbantke, Relativity, Groups, Particles, Springer, Wien (2001).

Very interesting book, thank you for pointing it out.

 

[haushofer]

You can check out the excellent lecture notes of David Tong. I also like For The Gifted Amateur; if that's too complicated, you probably should spend your time differently ;)

I also love Zee's book on Group Theory. He emphasises intuition instead of technical details, which for me personally is the best road to travel. It's actually fun to read.

 

[vanhees71]

My newest favorite as an introductory textbook:

B. G. Chen et al (Eds.), Quantum Field Theory Lectures of Sidney Coleman, World Scientific (2019)

It's really "as simple as possible but not simpler"!

 

[DrClaude]

My newest favorite as an introductory textbook:

B. G. Chen et al (Eds.), Quantum Field Theory Lectures of Bryan Coleman, World Scientific (2019)

It's really "as simple as possible but not simpler"!

Sidney, not Bryan

 

[vanhees71]

Of course, how did I come up with this? :-(. I've corrected it in the previous posting.

 

[Steve4Physics]

My newest favorite as an introductory textbook:

B. G. Chen et al (Eds.), Quantum Field Theory Lectures of Sidney Coleman, World Scientific (2019)

It's really "as simple as possible but not simpler"!

Despite my (extensive) level of ignorance of QFT, may I note that the 1975/6 series of Sidney Coleman lectures can be found here: https://www.youtube.com/watch?v=IRDpW7QOyGw&list=PLXjpiiAr8QGJlbPobSQBndPEx7lqV5xD0
Unfortunately the image quality is poor and the writing on the blackboard is generally impossible to read.

Also, notes by Brian Hill, - edited by Chen and Ting - for the first half of the 1986/7 lecture series can be found here: https://arxiv.org/pdf/1110.5013.pdf

 

[physicsworks]

Despite my (extensive) level of ignorance of QFT, may I note that the 1975/6 series of Sidney Coleman lectures can be found here: https://www.youtube.com/watch?v=IRDpW7QOyGw&list=PLXjpiiAr8QGJlbPobSQBndPEx7lqV5xD0
Unfortunately the image quality is poor and the writing on the blackboard is generally impossible to read.

Yes, someone should finally start working on a remastered version of these video lectures, instead of producing yet another blu-ray extended super-duper edition of "you_name_it" from the "year_X".