Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New features!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

122 submissions , 103 unreviewed
3,497 questions , 1,172 unanswered
4,548 answers , 19,352 comments
1,470 users with positive rep
409 active unimported users
More ...

Textbook on group theory to be able to start QFT

+ 1 like - 0 dislike
851 views

I am very enthusiastic about learning QFT. How much group theory would I need to master? Please could you recommend me a textbook on group theory, which would help me to start QFT?


This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user ramanujan_dirac

asked Apr 8, 2012 in Resources and References by ramanujan_dirac (235 points) [ revision history ]
recategorized Apr 24, 2014 by dimension10
There is a list here. I would also recommend Differential Geometry and Lie Groups for Physicists and Group Theory: A Physicist's Survey

This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user Vijay Murthy
Cross-listed to theoreticalphysics.stackexchange.com/q/1105/189

This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user Qmechanic
Closed as off-topic + cross-listed.

This post has been migrated from (A51.SE)
Cross-listed from http://physics.stackexchange.com/q/23387/2451

This post has been migrated from (A51.SE)

4 Answers

+ 3 like - 0 dislike

If you are interested more in physics than maths then I recommend: http://www.amazon.com/Lie-Algebras-Particle-Physics-Frontiers/dp/0738202339 as a start.

This post has been migrated from (A51.SE)
answered Apr 8, 2012 by Kyle (335 points) [ no revision ]
+ 2 like - 0 dislike

Georgi's book on Lie Groups is enough, but most of the group theory is explained in the physics texts. It is nice to learn group theory, but the mathematician's theory is more concerned with characters and root lattices, which are nice, but not essential in most of the bread-and-butter applications. The ALE classification is important in mathematical physics, but I think it is covered properly in the physics literature.

You don't need anything too special--- just the rudiments of Lie groups (it doesn't hurt to know group theory, though, it is just not essential). You can learn everything on your own from the QFT source and thinking it out--- there SU(2)/SU(3) cases are not too bad, and these are about as big as it gets. SU(5) and E8 require more sophistication, but are best covered in GUT papers and Green/Schwarz/Witten (for a great introduction to E8)

The modern algebra you probably want to learn is not group theory, but homological algebra, category theory, and Hopf algebra. These are covered well by Lang's algebra book, which is a graduate school staple in mathematics. It doesn't hurt to know everything in Lang--- it's well written, as everything by Lang--- although a little philosophically annoying for me, because it is so conservative in its set-theoretic appratus.

This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user Ron Maimon
answered Apr 8, 2012 by Ron Maimon (7,295 points) [ no revision ]
+ 1 like - 0 dislike

Actually to start learning the basics of QFT you do not need so much group theory [a different thing is if you want to go to the details]. Some of the introductory books in QFT have at the beginning a section about Lorentz and Poincaré groups, scalar, tensor and spinor representation etc. This is the case, for example in Maggiore, A Modern Introduction to Quantum Field Theory.

If you want group theory for physics for its own sake [which I find useful and beautiful] you may want to learn Lie groups and representations. Start with the link given by Vijay Murthy. There are also very good courses in the internet, I can recommend you some if you want.

This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user DaniH
answered Apr 8, 2012 by DaniH (60 points) [ no revision ]
+ 0 like - 0 dislike

Contemporary Abstract Algebra by Joseph Gallian is a good introduction to group theory.

This post imported from StackExchange Physics at 2014-03-24 04:54 (UCT), posted by SE-user Vafa Khalighi
answered Apr 8, 2012 by Vafa Khalighi (0 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ys$\varnothing$csOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...