How do I move from QM to QFT and beyond?

[taylrl3]

Hi,

I have now finished University where I took an advanced quantum mechanics module in my final undergraduate year. Having left I was quite surprised to find out that this is infact only a grounding in the subject and I would like to know more. I have covered operators and the Hamiltonian and perturbation theory but am looking for somewhere to learn more about QFT ideally. I love the Leonard Susskind lectures on youtube/itunes and was wondering if there might be any similar resources I could use to teach myself more. Also any suggestions of books that are good to work with would be much appreciated.

Many Thanks!

 

[Polyrhythmic]

"Quantum Field Theory" by Srednicki is an excellent introduction to the subject. You can find a draft of the book here: http://web.physics.ucsb.edu/~mark/qft.html

 

[vanhees71]

I'm not so enthusiastic about Srednicky. Why is he treating $\phi^3$ theory, which is not stable to begin with?

I'd rather recommend to first read Ryder as an introduction to get familiar with the concepts of both the operator and the path-integral formulation of relativistic QFT. Then, to really understand the subject from first principles, I'd take Weinberg, QT of Fields (3 vols.).

 

[Polyrhythmic]

I'm not so enthusiastic about Srednicky. Why is he treating $\phi^3$ theory, which is not stable to begin with?

That's because it is a simple theory which allows one to understand fundamental concepts of QFT in a direct way. Physical models are treated in later chapters.

 

[bapowell]

"Quantum Field Theory" by Mandl and Shaw is a gentle introduction. I second the recommendation of Ryder as well.

 

[vanhees71]

I understand the didactical reason behind the choice of $\phi^3$ theory (best in 6 dimensions, not to have an even superrenormalizable theory), but as many didactical choices it's not good at all! It gives up one of the most fundamental assumptions of QFT, namely that the Hamiltonian should be bounded from below and that there should be a stable ground state. Why isn't he using $\phi^4$ theory, which is not much more complicated and at least hasn't this verfy fundamental trouble (although it has other deficiencies)?

 

[dextercioby]

The first volume of Weinberg's book provides the necessary bridge b/w an advanced course on QM and a rigorous treatment of QFT, but one should be prepared with some extra mathematical skills such as group theory and differential geometry to keep up with the author.

 

[bapowell]

The first volume of Weinberg's book provides the necessary bridge b/w an advanced course on QM and a rigorous treatment of QFT, but one should be prepared with some extra mathematical skills such as group theory and differential geometry to keep up with the author.

All the more reason not to start with Weinberg. QFT is a dense subject with some important new concepts. If Wienberg requires differential geometry as a prereq, then his treatment sounds like it runs the risk of sacrificing clarity for rigor and completeness. I agree that group theory is a must; while I wouldn't recommend Kaku's "Quantum Field Theory" as a general text, his group theory discussion is decent enough to get the ball rolling. Also, Ryder introduces those aspects of Lie groups that are pertinent to his development.

 

[muppet]

It's just about possible to follow Weinberg's discussion of representations of the Lorentz group without much knowledge of group theory or diff geom, but it'll be much much easier if you have it; and to get very far in modern physics you'll need to learn it eventually! Something like the first two chapters of Georgi's book is more than enough to get going.

Before you even get to QFT, there's certain concepts you need to have a solid grasp of already. "Operators, the hamiltonian and perturbation theory" could be regarded as only basic QM; I'd advise looking at the first couple of chapters of e.g. Sakurai's book (or similar) to make sure that you have a reasonable grasp of the basics- state vectors, the significance of hermitian and unitary operators, time evolution and the like. I mention Sakurai's book specifically as he intended it as preparation for learning QFT, so he includes treatments of things like path integrals and propagators that you don't generally meet in undergraduate treatments of QM. For scattering, I'd strongly recommend the book "Quantum theory of nonrelativistic collisions" by Taylor, for very clear and careful explanations of concepts like the S-matrix and the scattering cross-section, the calculation of which is what 90% of QFT boils down to.
There's also classical physics to consider- Lagrangian/Hamiltonian formulations of classical mechanics, and the explicitly Lorentz invariant formulation of electrodynamics.

As for actual quantum field theory texts, I think most people find that they have to look at more than one text for it all to sink in; someone recommended to me a combination of the books by Zee and by Srednicki, and it seems to me that that could work well; both books feature the path integral formalism prominently early on, Zee's has nice conversational style and good pedagogical explanations, and all calculations are presented in the simplest possible way, whilst Srednicki's seems better for actually learning how to calculate things, and using grown-up language (the index of Zee's book won't shed any light on "one-particle-irreducible" diagrams, for example). (A free draft of Srednicki's book is also available online, and at the start features a list of equations you should recognise and understand as a test to see if your prerequisites are up to starting QFT!)

 

[vanhees71]

Zee's book is very superficial. I think it's fun to read, if you know the subject but not carefully enough formulated to understand how qft works.

If you prefer an early use of path integrals, I'd recommend Bailin, Love Introduction to Gauge Field Theories.