Particle physics mathematics

[shekler]

Any suggestions on text which could better my understanding of the mathematics governing particle physics? I am in my fourth year of my B.A.Sc. engineering physics degree, so I have a fairly strong math background as is.

Thanks in advance.

[JasonJo]

Any suggestions on text which could better my understanding of the mathematics governing particle physics? I am in my fourth year of my B.A.Sc. engineering physics degree, so I have a fairly strong math background as is.

Thanks in advance.

I don't think an engineering background is enough math for particle physics. From my understanding, a lot of particle physics is modeled on gauge theories and the SU(n) objects. I know a lot of Lie Algebras are used.

[jdstokes]

For particle physics you want to understand the representation theory of compact matrix Lie groups, in particular SU(N) and how particle multiplets fall into their representations such as the singlet, fundamental and adjoint representations. Understand how to obtain higher dimensional representations from the fundamental representation using the tensor method.

For physics books, have a look at Cheng and Li which talks about the tensor method and Young tableux. For pure maths check out Wu-Ki Tung Group theory in physics. There is also a GTM book by Brian Hall on Lie groups.

Edit: Of course, you should already know all about the Dirac equation and quantum field theory first.

[Vanadium 50]

I'm going to disagree with the above two posts. While Lie groups play an important role in particle physics, actually doing a calculation requiring deep understanding of them is rare and specialized. Somebody did the algebra a long time ago, and now we can just use the results. (A classic example is Clebsch-Gordon coefficients)

I would say that of you have a good solid class on linear algebra - i.e. one that includes basic elements of abstract in it, not just "calculational tricks for solving systems of equations" - you'll know enough.

[Monocles]

Hmmmm, I have sort of a similar question. I'm a 2nd year physics undergrad and I was going to double major in math so I wasn't really worried about getting all the math classes in that I need, but upon reviewing how much extra it would cost me to take a 5th year I'm reconsidering. I'm interested in plasma and high energy. I made a thread for what I should take if I wanted to do plasma physics in grad school, but what about high energy? Right now all I will have after this fall is calc 1-3, diff eq, and abstract vector spaces (proofs-based linear algebra class, intro linear algebra was included in calc 2).

[shekler]

I don't think an engineering background is enough math for particle physics. From my understanding, a lot of particle physics is modeled on gauge theories and the SU(n) objects. I know a lot of Lie Algebras are used.

I mentioned my engineering physics background to give an idea of my ability to comprehend the math, not to suggest that I know the material already. Thanks for the replies everyone!

[mgiddy911]

I would suggest you need a broad knowledge of topics. If you want to do the computational side of particle physics then you need to have some skill in running numerical calculations, ie. Matlab, ROOT, numerical analysis... etc.

If you are into the theory side then having a working understanding of abstract algebra, group theory, and linear algebra should be sufficient for beginning.

Of course that just covers the maths. You need a lot of physics knowledge before you dive into Particle Physics. A good class on modern physics, E&M, Theo. Mechanics, and maybe also QM will be good for starters

[qualgorithm]

Hmmmm, I have sort of a similar question. I'm a 2nd year physics undergrad and I was going to double major in math so I wasn't really worried about getting all the math classes in that I need, but upon reviewing how much extra it would cost me to take a 5th year I'm reconsidering. I'm interested in plasma and high energy. I made a thread for what I should take if I wanted to do plasma physics in grad school, but what about high energy? Right now all I will have after this fall is calc 1-3, diff eq, and abstract vector spaces (proofs-based linear algebra class, intro linear algebra was included in calc 2).You don't need a B.A. in Mathematics to do high energy physics. Sure, it never hurts to take more math classes, but most of what you need you can get from a physics perspective. You don't need much more math than that for your physics degree. Useful additions from the math department might include abstract algebra and complex analysis. Or just talk to the physics profs at your school.