What Are the Best Resources for Studying Branes and M-Theory?

[tom12519]

For part of a school research project I have to write a "paper" on a research topic of my choice. I have chosen branes and m-theory as my area to focus on. However, I would appreciate any thoughts, recommendations and general advice on what to do. So far I have begun learning the associated mathematics (vector and tensor analysis among other things) to be able to handle such things. However, is there anything anybody could seriously recommend for learning about such areas? I intend to cover some special relativity, general relativity and then move into Brans-Dicke gravitation and ekpyrotic brane collision theory - although nothing *too* complex. I appreciate any input on it, thank you.

Edit:
(Darn, could this be moved to homework section? Thank you)

 

[cristo]

What level in "school" are you? I severely doubt that such a topic will be suitable for you to write a research paper on, unless of course it doesn't need any maths, and is purely "popular" science.

 

[tom12519]

I am currently in year 12, and it's not entirely appropriate. But I don't want to do something that bores me. I am currently acquiring all the appropriate knowledge mathematically. It is also not a research paper, per se, but more just a lengthy project to expand my horizons. Any help that you could offer into the subject?

 

[trinitron]

Here is a good guide to the mathematics that you will need: http://superstringtheory.com/math/math2.html

As far as physics, I assume that you should be familiar with GR and quantum field theory before you begin learning string theory.

 

[mgiddy911]

Year 12? as in Senior in High School?
If that is the case are you sure you are really currently acquiring all the appropriate knowledge mathematically?

 

[maverick280857]

You said paper on a research topic, and not a research paper. There is a distinction of course.

Anyway, I suppose you should have a look at Brian Greene's book "The Elegant Universe" first. That will build up the motivation for string theory, M Theory and D-Branes. Then, you can back it up by reading historical developments esp seminal paper presentations/conferences, etc. You can also read some mathematics/physics in parallel, although as cristo and trinitron have pointed out, there is a fair amount involved here (listed on the link trinitron gave you).

You should first be looking at writing a purely original expository article which anyone at your level (year 12) can understand. Then, you can add rigor by using mathematics if necessary. What kind of paper does this have to be anyway?

(If it has to be from any field in physics--theory or experiment--unless the paper has to be at a pop-sci level, there will be some mathematics and probably graphs/figures necessary. The key is to be able to understand them well enough for your project. A deep understanding will require a lot more math/physics.)

You should look at and highlight (a) solved problems, (b) open problems and conceptual issues pending attention/analysis in the field. These may require looking at research papers and review articles which will be a research task in itself.

 

[cristo]

One of the most important problems you are faced when given such an assignment is picking something that is achievable: I really think that this topic is not, unless you have a couple of years to learn the preparatory material for it. I also think that you are more likely to get a better mark for writing a good paper on a lower level topic than a bad paper on a topic that was way too hard for you to understand. I mean, sure, you can reproduce Brian Greene's book, but then I somehow don't think that is the point of the assignment.

You should look at and highlight (a) solved problems, (b) open problems and conceptual issues pending attention/analysis in the field.

Are there any solved problems? Are the open problems even going to be comprehensible by someone who has no idea about the field?

I think you should find something more achievable to write about. What is the actual assignment you are given? Perhaps we'll be able to suggest something else that will enable you to succeed!

 

[maverick280857]

Are there any solved problems? Are the open problems even going to be comprehensible by someone who has no idea about the field?

I didn't mean that he should reproduce that book or present his report the way a pop-sci book is written. I think its possible to understand some open problems provided they are worded in a manner that is comprehensible to those who have limited or no technical knowledge of the field. I cited Brian Greene's book as an example to illustrate this fact...in fact his other book "The Fabric Of the Cosmos" is more diverse in its coverage.

So for instance, as general relativity uses differential geometry to describe a smoothly evolving universe with curvature, redshift etc being continuous functions of time, how is this inconsistent with quantum mechanics? What principles (mathematically) of quantum physics does it violate? Why does a new theory (say M-Theory) appear promising to unify QM and general relativity? I know this is sounding more like a review/expository article.

Have you committed yourself to the topic or can you change it too? Have you considered other topics in physics, e.g. experiments, or other areas in theory? I agree with cristo about being able to write a comprehensive 'review of research' for this topic. But again, you have to tell us what kind of paper you have to write first.

PS--In year 12 in school, I would be surprised if they expect you to write a non-pop-sci article on an area you need a lot of background to understand...I never had such a project in my final year in school (Class 12 we call it here).

 

[muppet]

I intend to cover some special relativity, general relativity and then move into Brans-Dicke gravitation and ekpyrotic brane collision theory - although nothing *too* complex.

LOL.

I have no idea how much you actually know about this stuff. I consider myself a pretty nerdish undergraduate, and I've never heard of Brans-dicke gravitation or ekyprotic brane collision theory- so kudos! But if you're still at school, and you haven't even studied any proper special relativity yet, then to attempt a mathematical treatment of M-theory is beyond ambitious. You might have started to learn tensor calculus (again, that's impressive if you've made a serious attempt at it) but if you really intend to work your way through tensor calculus, special relativity, differential geometry, general relativity, and quantum field theory- and we haven't even mentioned a 1D string yet- don't plan on finishing this year.
If you don't have to include maths, then M-theory might be something you could talk about in qualitative terms. But I very much doubt that to learn everything you need to know is achievable in such a short timeframe. Have you already taught yourself virtually the entirety of both maths and further maths A-level? Because without already knowing single variable calculus and matrices inside out I don't see how you could begin to seriously attempt even what you claim to have started.
As another thought- unless your teacher has at least an MSci in this specific area, he won't be able to understand your paper. He'd have to be a very trusting teacher to assume you hadn't made half of it up!
If you're desperate to do a mathsy paper, I'd say that ordinary quantum mechanics or just special relativity would be hard enough to tax even an extremely bright school student. If you're 16 years old and you find mathematical treatments of those topics boringly easy, I seriously look forward to your Nobel acceptance speech.