Prerequisites for Quantum Field Theory (QFT)

[soviet1100]

Hi!

I'm desperately trying to develop a list of prerequisites that will enable me to work on topics like quantum gravity, advanced QFT (on curved spacetime etc.) etc. I am currently in the second year of an undergrad theoretical physics degree in the UK, and am heavily unsatisfied with the way the programme is organised, especially for prospective theorists.

As of this moment, I know these topics (more or less),
1. Special Relativity at the level of Spacetime Physics - Taylor, Wheeler
2. Classical Mechanics (including waves & vibrations) at the level of Physics - Resnick, Halliday, Krane
3. Mathematics (Linear Algebra, ODEs & PDEs, Single & multi variable calculus, Fourier analysis)
4. Quantum Mechanics at a slightly higher level than Intro to Quantum Mechanics - Griffiths
5. Electromagnetism at a slightly higher level than Electricity & Magnetism - EM Purcell
6. Other extras such as Atomic & Nuclear Physics, thermodynamics & statistical mechanics, elementary astrophysics, optics, solid state physics

I require a list of topics (in mathematics and physics) I need to know that will get me ready to start a PhD in particle theory. Comments on the level of study required in each topic (e.g. at the level of this textbook) would also be helpful.

Thanks!

 

[dx]

If you have studied all the things that you listed, you are almost ready to begin studying quantum field theory and general relativity. You did not list group theory and complex analysis, so you would have to learn those first. Also you have to learn special relativity to a slightly higher level than spacetime physics by wheeler. Do you know the relativistic formulation of electrodynamics in therms of the faraday tensor F? You have to learn special relativity to that level. Also, have you studied Lagrangian and Hamiltonian mechanics? You have to learn those also.

Quantum Mechanics:
(you have to know about operators and Dirac's bra-ket notiation. I don't know if Griffiths covers those.)

1. Feynman lectures, Volume III.
2. Principles of Quantum Mechanics, Shanker
3. Leonard susskind has nice lectures on youtube, and also a book with Art Freidman. This is good for a first exposure if you are not familiar with bra-ket and operators etc.
Advanced classical mechanics:

1. Landau "mechanics" (very good and short)
2. Arnold, "mathematical methods of classical mechanics" (you should look at this once you learn differential geometry and calculus on manifolds, for example in MTW listed below for GR. This is not strictly necessary to learn QFT, but it is a good idea to learn it early, if you want to do research in theoretical physics. You have to learn it eventually anyway, and certainly if you want to work on quantum gravity)

Complex Analysis:
1. Visual Complex Analysis, Needham
2. Complex analysis, Ahlfors
3. Infinitesimal Calculus, Dieudonne

Once you learn quantum field theory and general relativity, you will be in a position to start a PhD in particle theory. Here are some books that you could look at for those subjects:

QFT:

0. Quantum Field theory in a Nutshell, A Zee
1. Peskin & Schroeder
2. Introduction to Gauge Field Theory, by Bailin and Love
3. Field Theory, Ramond
4. Quantum Theory of Fields, Weinberg (advanced)
5. Global Approach to Quantum Field Theory, deWitt (very advanced but good to look at after you learn QFT)
6. Quantum Field Theory, Srednicki
7. Quantum Field Theory, Itzukson and Zuber (slightly advanced, but also a little old)

GR:

1. Misner Thorne Wheeler
2. Wald

These GR books are not good for a first exposure, unless your mathematics is really good. but you will have to know GR at the level of these books by the time you start your PhD. There are other less advanced books, like Schutz.

 

[bhobba]

I am going to take a different view here.

Recently a number of books have stared to appear that allow the study of QFT at the undergrad level after just a first course in QM with a book like Griffiths or even Susskinds:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

Here is the one I have:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Other than that I would simply suggest a smattering of special relativity (which you have) eg:
https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

Not that mad keen on Spacetime physics by Wheeler - it always looked rather 'pokey' to me - although good for developing intuition - but I am not sure intuition is what's needed in QFT.

Start with a book like the Gifted Amateur one and pick up what you need as you go along - eg group theory. Then proceed to more advanced books like Zee, Srednicki etc, then the holey grail - Weinberg's three volumes which, to put it mildly, are rather challenging.

For GR I would start with something like Relativity Demystified:
https://www.amazon.com/dp/0071455450/?tag=pfamazon01-20

Actually his book on QFT isn't a bad place to start before proceeding to books like the Gifted Amateur:
https://www.amazon.com/dp/0071543821/?tag=pfamazon01-20

Then proceed to Schutz, then Carroll, then Wald. Personally I like Wald better than MTW - it has a higher standard of mathematical rigour. But that's just me.

It's more perseverance IMHO than ensuring you have dotted all the i's and crossed the t's in the prerequisite department.

Thanks
Bill

 

[bhobba]

1. Landau "mechanics" (very good and short)

Superb book - not known widely enough IMHO:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20
'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.'

It will change your view of physics and teach you to think like a theoretical physicist - or in my case, since my background is math, like a mathematical physicist. Either way your understanding of what physics really IS will likely never be the same again. Enough said.

Thanks
Bill

 

[dx]

Yes, and whatever you do, stay away from Herbert Goldstein's "classical mechanics" at all costs!

 

[atyy]

Yes, and whatever you do, stay away from Herbert Goldstein's "classical mechanics" at all costs!

Even the sections on continuum mechanics? I was told Goldstein is only bad because the really good part is at the end, but no one has the stamina to make it there! (I've never read it, since I'm not a professional, I took the easy route with Fetter and Walecka.)

 

[dx]

It may be true that the sections on continuum mechanics are good. I didn't read that part of the book. But the discussions in the beginning chapters, particularly the calculus of variations manipulations, constraints, holonomic and anholonomic etc. are very confusing if one doesn't already know what's going on.

 

[bhobba]

Yes, and whatever you do, stay away from Herbert Goldstein's "classical mechanics" at all costs!

Too true, too true.

Thanks
Bill

 

[marcom]

https://fliptomato.wordpress.com/2006/12/30/from-griffiths-to-peskin-a-lit-review-for-beginners/

 

[soviet1100]

Thanks to everyone for the comments. I have studied the Dirac formalism to great detail. I actually used Principles of Quantum Mechanics by R.Shankar as my first text on QM. However, I still haven't read the latter parts of the book (chapters on spin and forward). These concepts, I studied from Griffiths (was short of time). So the knowledge that I've retained is slightly higher than that gained from Griffiths alone, which I must say is a very poor text compared to Shankar.

I do have Lancaster's book (QFT for the gifted amateur), bhobba. I'm trying to fill the prerequisite holes specifically to start study of that book (only QED) within a month's time. Lancaster spends a few pages on the prerequisites (relativity in the zeroth chapter, overture; lagrangians in the second) but I suppose he expects the reader to be acquainted with these concepts before study of the book.

I have effectively no experience with group theory, tensors, complex analysis, and Lagrangian & Hamiltonian formalisms of classical mechanics.

As for special relativity (have read Taylor & Wheeler), is there a very concise read (notes or a book) that will enable me to cover the QFT prerequisites in this area within a few days (of full study)?

I do own a copy of Landau's Classical Mechanics and have deep appreciation for Landau's texts. His style is not atypical of Russian writers in physics and mathematics. You may find many such golden gems here - mirtitles.org (not a violation of copyright as Mir publishers closed down after the collapse of the Soviet Union and no one claimed publishing rights for the books on the website).

However, I'm surprised at the unanimous disapproval of Goldstein's text. Isn't that the 'gold standard'? Doesn't Goldstein cover more material than Landau? Is Landau's Classical mechanics sufficient as a first and last read on the subject, to progress to QFT? (I do intend on reading V.I. Arnold's geometric treatment of CM as well, but not in the immediate future)

I have copies of the classic complex analysis texts by Ahlfors, Needham, Howie. However, these books are time consuming to read and I need to muster the prerequisites for QED (in Lancaster's book) within a very short time. In light of this complication, will the relevant chapters on complex analysis, group theory, and tensors from Boas suffice?
I can study the required maths as I go along, but I've found it extremely frustrating to do it that way, especially when the mathematical inadequacy gets in the way of understanding the physical concepts.

Also, as an extra, any general comments on D'inverno's text in comparison to other standard introductory GR texts? Does it give you an introduction to differential geometry or calculus on manifolds? In this regard, will Schutz's Geometrical methods of mathematical physicists suffice as an introduction to this topic and enable me to study the subject more rigorously from Spivak's 5 vol. treatise for example?

Thanks again for all the help

 

[dx]

Boas is good enough for complex analysis and group theory, if you want to quickly get to QFT.

But my advice is don't rush through special relativity and tensors. It is important to learn these properly. Look at this book:
http://www.nrbook.com/relativity/

If you can do all the problems in the first 6 chapters, that will be good preparation.

 

[bhobba]

I do have Lancaster's book (QFT for the gifted amateur), bhobba. I'm trying to fill the prerequisite holes specifically to start study of that book (only QED) within a month's time. Lancaster spends a few pages on the prerequisites (relativity in the zeroth chapter, overture; lagrangians in the second) but I suppose he expects the reader to be acquainted with these concepts before study of the book.

With that book it would be nice - but not necessary - he explains it pretty well.

Thanks
Bill

 

[soviet1100]

Thanks again. I also looked at Benjamin Crowell's Special Relativity text. It seems to be the most comprehensive standalone treatment of the subject I've seen at the undergraduate level. There's also another advanced book, Special Relativity in General Frames by Eric Gourgoulhon, which seems superb but unfortunately, I have to save it for a future read. I'm planning to work through Crowell's text to cover my prerequisites for QFT in the SR department.

As for QFT itself, I've noticed that the sections in Lancaster's book are devastatingly brief. I haven't started working through the book yet, but I have the premonition that another standard text will be needed, both to fully understand the material and to study the topics comprehensively. I've decided to go for either Peskin & Schroeder or M Schwartz (QFT & the Standard Model). I'm aware of the ridiculous number of typos in P&S, but there is an errata online. Could anyone compare these two books, especially their appeal for beginners in the subject?

 

[bhobba]

I've decided to go for either Peskin & Schroeder

Don't start with that - it's well known as an excellent reference - but hard and advanced.

Start with Lancaster. The chapters are short because he uses a many small steps approach. For example Lancaster explains the Lagrangian approach in a chapter - but really at this level you should know it - however he doesn't assume such which is why its a good book to start with - its less demanding on perquisite knowledge and goes at a more leisurely pace. After Lancaster you can move onto the more advanced texts like Peskin & Schroeder but I would then do a book like Zee.

Thanks
Bill

 

[vanhees71]

I still haven't worked with Schwartz's text in detail, but from reading in it a bit I think it's a very good book to begin with. Peskin Schroeder is not only full of typos but is sometimes a bit too sloppy. There are indeed dimensionful arguments in logarithms ironically in the chapter on the renormalization group. That's a real pity, because in principle it's a very good book, explaining also how to calculate Feynman diagrams in dim. reg. in some detail, which is very helpful, since QFT looses much of its difficulties by really doing calculations.

 

[soviet1100]

Start with Lancaster. The chapters are short because he uses a many small steps approach. For example Lancaster explains the Lagrangian approach in a chapter - but really at this level you should know it - however he doesn't assume such which is why its a good book to start with - its less demanding on perquisite knowledge and goes at a more leisurely pace. After Lancaster you can move onto the more advanced texts like Peskin & Schroeder but I would then do a book like Zee.

Thanks. I'll use Lancaster as the main book. I suppose that would prepare me for P&S or Schwartz. I've had a look at Zee, can't say I like it too much.

I still haven't worked with Schwartz's text in detail, but from reading in it a bit I think it's a very good book to begin with. Peskin Schroeder is not only full of typos but is sometimes a bit too sloppy. There are indeed dimensionful arguments in logarithms ironically in the chapter on the renormalization group. That's a real pity, because in principle it's a very good book, explaining also how to calculate Feynman diagrams in dim. reg. in some detail, which is very helpful, since QFT looses much of its difficulties by really doing calculations.

Yes, the list of errata for P&S is ridiculously long. The structure of Schwartz also seems more appealing. Thanks for the help.