Required Mathematics for Theoretical Particle Physics

[K.J.Healey]

I'll be starting my PhD this fall, and I intend on entering the field of Theoretical Particle Physics. I was just wondering what I could do to get a head start in the next two months that would help me secure some positions for research within the school.
I figure I'd need to pick up a book on whatever mathematic basis is mainly used for theoretical and experimental research to enable me to pick up the newest articles and have a chance at understanding their contents.

I also wonder what resources there are online with which I could educate myself more quickly on particle physics. I have a decent understanding of the overview of particles and their interacitons. I'm not looking for something basic. I'm looking for something that, once I learn the mathematics needed, I can begin learning immediately in a very in-depth manner.

My mathematics background now is up to and including Partial DiffEq(BVP,etc), a basic Linear Algebra, and Complex Analysis. I'm currently reading a textbook on Algebraic Topology and set theory that I felt I should know, if only as a base. What other mathematics are used that I should pick up on my own?

As you can see, its the tools(math) to learn the material that I'm primarily concerned with, not the material (physics) itself. I have no doubt I can understand almost anything so long as I understand the notation used to describe it.

 

[K.J.Healey]

Seems that knowing some Lie Group theory would help. Is there some course/book that would cover that on after basic algebraic topolgy (seems the text i have doesn't specifically talk about it much)

 

[humanino]

It depends what precise PhD topic you want to do. If you want to do quantum gravity, then sure, Algebraic Topology is useful. But then you should go talk about that in the other thread I guess If you want to do supersymetry, Lie Group theory is mandatory... So what are you interested in ?

 

[K.J.Healey]

Hmm, am I limited to what faculty at my university are currently researching? Or do they care if I try to branch them into something new? (In General)

Also, I see the required courses for the PhD degree; should I expect them to expect me to take additional mathematics to supplement the physics courses? Is this something that is usually taken care of by the university during consulatation with your advisor, or something where I should take the initiative and plan out a proper course of action.

I'll do some quick research and see what my department is doing in terms of current research. I have a general idea but I'm wondering if there are any newer fields that are closely related that my school hasn't had the oppurtunity to approach yet. Are there any sources that have a decent list of possibilities or rather the different branches of research and perhaps how they connect to each other?

 

[humanino]

Hmm, am I limited to what faculty at my university are currently researching? Or do they care if I try to branch them into something new? (In General)

It seems unlikely to me that you will convince them to support you if you go in a remotely disconnected activity.

Also, I see the required courses for the PhD degree; should I expect them to expect me to take additional mathematics to supplement the physics courses?

You should ask them in person. I guess you should indeed take those courses, if the timing allows you.

Are there any sources that have a decent list of possibilities or rather the different branches of research and perhaps how they connect to each other?

Not that I know of. You can browse the ArXiV to see the most active topics lately.

Good luck in any case