How much more math/physics do I need to learn before I can read this article?

[Credulous]

Specifically what Physics subjects and what mathematical techniques come into play that I would need to learn in order to comprehend it?

I am currently in sophomore level undergrad physics (this year we covered waves, optics, ordinary differential equations, electromagnetism again, ect). I have taken the general (American) curriculum in math up to real analysis and abstract algebra.

I just want to know what I would have to study because to me the ability to just grab papers off of arxiv to read would be one of the greatest pleasures ever.

 

[ljus]

Which article mate?

 

[Credulous]

Which article mate?

whoops! This article that I found on arxiv: http://arxiv.org/abs/1204.0351

 

[Redsummers]

I just took a glimpse to the paper, and it seems like you need tensor analysis, functional analysis, differential geometry/topology (I see a lot of references from Kirillov) and just by the title I'd also go with 'advanced quantum field theory'. So to answer your question: 'quite a lot'. Bear in mind that arXiv articles are normally aimed for specialists in their own fields, it's hard to try and understand them while doing one's bachelor.

Also, I think it might be more sensible to study the subjects themselves by their own, instead of studying sub-parts of each subject just to understand the article.

 

[Desordre]

Bear in mind that arXiv articles are normally aimed for specialists in their own fields, it's hard to try and understand them while doing one's bachelor.

Dear Red,
it makes me think of a related question: where to find articles that are suitable for undergraduate reading?

Desordre.

 

[Redsummers]

Dear Red,
it makes me think of a related question: where to find articles that are suitable for undergraduate reading?

Desordre.

You can certainly find some articles in arXiv aimed for bachelor students (normally, such articles are titled like 'introduction to...'). But preferably, if you want to see some 'new' research being done in the paper, it might be better to search for papers written by other undergraduates. Of course, I don't know you, but you are probably interested in a particular field of physics and maybe you are member of a seminar group, etc. In this case, you can ask your professor for suitable papers to read. I know my bachelor supervisor gave me papers to read from the 70s and I much enjoyed reading them with my basic knowledge of differential geometry and lie algebras.
Sometimes, it is also a good idea to just grab a bachelor/master thesis and read it, for they tend to be self-contained and try to explain the mathematical preliminaries needed to understand the thesis. You should be able to find an archive of bachelor/master thesis in your dept. website. The downside to this is that you don't get to do exercices! and it is always important to do problems by oneself to really master a subject. However, if you want to get a 'general picture' of the subject, it is still recommendable to just read them.

 

[Desordre]

Dear Red,
actually, I'm coming from an unrelated field directly to the core (or must I say, hardcore) of pure maths. So, for the time being, I am not part of any group, something I miss. But the idea of "introduction to" and undergrad papers is cool. I will look for that.
Best wishes,
Ds.

 

[twofish-quant]

Specifically what Physics subjects and what mathematical techniques come into play that I would need to learn in order to comprehend it?

It looks like first year graduate student stuff. By the time you finish your undergrad, you should know enough so that parts of the article will make sense.

I just want to know what I would have to study because to me the ability to just grab papers off of arxiv to read would be one of the greatest pleasures ever.

Standard undergraduate physics curriculum should make the article partly comprehensible.

The important mathematical concepts are:

1) green functions
2) functional analysis

The important physics concepts are:

1) partition functions
2) action principle
3) some general relativity

 

[twofish-quant]

Dear Red,
it makes me think of a related question: where to find articles that are suitable for undergraduate reading?

Desordre.

Probably you'd do well to attend a journal club, especially one in which people are presenting results to people in other areas of physics.

One issue is that articles aren't set up for teaching purposes. I'm pretty sure that you could take the article that the OP brought up, and then "gloss" it so that it's comprehensible to junior level undergraduate physics majors, although I don't know of anyone that is doing anything like that. Journal clubs are the closest thing I can think of to a gloss.

 

[Desordre]

Dear Twofish,
actually, I'm not looking for articles with a pedagogical scope, but rather to understand how do someone do write a paper in the mathematical field.

The idea of a journal club is interesting. I must look for some or other related gatherings.


Ds.

 

[twofish-quant]

Actually, I'm not looking for articles with a pedagogical scope, but rather to understand how do someone do write a paper in the mathematical field.

You can think of journal articles as parts of a conversation. If you are in a foreign country and someone in a restaurant says something to you, you don't know how to reply. Once you understand the language, and someone says something, then you can usually think of something that you also want to say in response.

That's why it's useful to "gloss" an actual research article. Once you understand what the conversation is about, and you've mastered the language, you can say something in reply.