Preparing for QFT: Best Way to Approach Non-Physics Student's Thesis

[Alesak]

Hi guys,
I need to get into QFT because of my thesis, yet I study nothing near physics so I need your guidance how to best proceed. I've got two questions, any answers appreciated:

1) how much QM should I learn? In my book (zettili) I'm in chapter about harmonic oscillator and the rest of the book seems to be occupied by topics such as angular momentum, perturbation theory and scattering theory. Are there any specific topics I should pay special attention to?

2) from other physics, I understand I need special relativity and EM. How much effort I should dedicate to these? Also, my classical mechanics is a bit basic, I know Hamiltons' equations and how to, say, solve simple harmonic oscilator with it, but nothing more advanced, such as Noethers' theorem.

3) the topic that interest me most is renormalization and gauge groups. Any comments how to best prepare for good understanding of these?

Thanks

 

[ZombieFeynman]

Hi guys,
I need to get into QFT because of my thesis, yet I study nothing near physics so I need your guidance how to best proceed. I've got two questions, any answers appreciated:

1) how much QM should I learn? In my book (zettili) I'm in chapter about harmonic oscillator and the rest of the book seems to be occupied by topics such as angular momentum, perturbation theory and scattering theory. Are there any specific topics I should pay special attention to?

2) from other physics, I understand I need special relativity and EM. How much effort I should dedicate to these? Also, my classical mechanics is a bit basic, I know Hamiltons' equations and how to, say, solve simple harmonic oscilator with it, but nothing more advanced, such as Noethers' theorem.

3) the topic that interest me most is renormalization and gauge groups. Any comments how to best prepare for good understanding of these?

Thanks

1. In principle, all of them. Zettilli is a good book, but a bit elementary. You should look into studying from merzbacher and shankar as well. All of the topics you mentioned are important, but in addition you should pay special attention to the path integral formulation of QM.

2, 3. QFT builds on significant pillars of classical physics. Particularly pay close attention to the use of gauges in classical EM field theory.

Any understanding of classical mechanics will be of use. You should be especially proficient with Lagranges Principle of Least Action, and the resulting lagrangian mechanics.

Knowledge of group theory will also be of use. This can be introduced to you via the study of angular momentum and spin in the study of tradi tional texts in QM

Im a bit curious as to why you need to know QFT for a subject not related to physics. Some have called it the crown jewel of physics. It truly builds on the entire subject.

 

[Alesak]

1. In principle, all of them. Zettilli is a good book, but a bit elementary. You should look into studying from merzbacher and shankar as well. All of the topics you mentioned are important, but in addition you should pay special attention to the path integral formulation of QM.

I got Shankar from the library and it's very good book as well. I use them both concurently, as for example Shankar has chapter on classical mechanics, but Zetillis' part on free particle contains useful information that Shankar did not. Or Shankar does harmonic oscilator with both approaches, while Zettili uses only ladder operators, and so on... If I had to pick one, it would be probably Shankar.

2, 3. QFT builds on significant pillars of classical physics. Particularly pay close attention to the use of gauges in classical EM field theory

I've got prepared Principles of Electrodynamics from Melvin Schwartz, and apparently the word "gauge" is used only once in the book. Do you have any favourite book that you would recommend?

Any understanding of classical mechanics will be of use. You should be especially proficient with Lagranges Principle of Least Action, and the resulting lagrangian mechanics.

Knowledge of group theory will also be of use. This can be introduced to you via the study of angular momentum and spin in the study of traditional texts in QM

Luckily group theory I've got covered, and Lagrangian mechanics won't be much problem for me since I've read Smooth manifolds from Lee. Apart from that, I know what Lie group and Lie algebra is, so it might make things easier down the road.

Im a bit curious as to why you need to know QFT for a subject not related to physics. Some have called it the crown jewel of physics. It truly builds on the entire subject.

Well, to tell the truth, I don't strictly need QFT. My thesis has a topic "Application of renormalization groups to financial market crashes", so as you can imagine, statistical mechanics would be fine too. But I take it as a good excuse to learn some more advanced physics, which I always wanted to, since renormalization group after all originated in QFT.

 

[Fredrik]

I would recommend that you try to read one of the easier QFT books, like Mandl & Shaw, and when you get stuck on something that involves relativity for example, you read up on that aspect of relativity.

If you're going to study QM and SR first, I recommend that you focus on what the theories say, and not so much on specific applications. When you study solutions of the Schrödinger equation, you will probably want to look at the particle in a box problem (because it's the easiest possible one) and the harmonic oscillator problem (because the creation/annihilation operators that you will encounter in QFT are very similar to the ladder operators used in the solution of the harmonic oscillator problem).

Study SR in terms of spacetime diagrams (e.g. by reading the first few chapters of Schutz's GR book). Then make sure that you understand the definition of matrix multiplication from linear algebra $(AB)_{ij}=\sum_k A_{ik} B_{kj}$, because you will have to use it a lot when you're dealing with algebraic aspects of Lorentz transformations in QFTs. You need to be able to handle the mess of indices that QFT students have to deal with. This post explains the notational convention for components of $\Lambda$, $\eta$ and $\eta^{-1}$.

I don't know what to recommend to get you to the renormalization group as quickly as possible.

 

[Alesak]

Thanks, very helpful.

If you're going to study QM and SR first, I recommend that you focus on what the theories say, and not so much on specific applications.

That's what I'm trying to do, and so far two most puzzling thing about QM are that momentum of a particle is fully determined by it's shape in space(meaning wave function in position representation) and that observables are operators, which is really an application of linear maps I'd have never imagined. I still need to think about it more and get what is this method about, in general.