# String Theory: Where to begin?

Hello,
I have read Brian Greene's book "The Elegant Universe" as well as a few other books and I have a fairly decent understanding of the Concepts of string theory, and I would like to start learning the actual physics and math behind it.

Could someone please point me in the right direction.
I would prefer an online source so that I don't have to actually purchase anything and I can begin right away.

Yes, I have searched on google, but all I could find is sites that assume you already know the basic equations or sites that simply describe the concepts (which I have read numerous times) I am looking for something that will give a beginners lecture on how to derive the approximate equations and apply them.

cristo
Staff Emeritus
How much Physics/Mathematics do you know? For example, have you studied relativity, quantum field theory, differential geometry,...? To study string theory, I'd say you'll need quite a strong mathematical background!

To be honest, I wouldn't bother unless you're already familiar with general relativity and quantum field theory. You won't be up to speed on the mathematics otherwise.

Well I have a grasp on relativity, not only was it well explained in "The elegant Universe", but I have done a lot of reading on it. online as well as in 2 different physics books that derive the relativity equations. My brother is currently majoring in physics in college for the second year, and my dad teaches Statistics and Calculus in highschool so I have a good deal of help at home. This is something that I really would like to learn about, so If you all recommend that I start with quantum field theory (having a confident understanding of relativity) than that is were I will begin. But, again, if this is what I should do, then links or ideas of where to start would be greatly appreciated, although I should be able to find help on that subject through google. Thanks.

cristo
Staff Emeritus
Well I have a grasp on relativity, not only was it well explained in "The elegant Universe", but I have done a lot of reading on it. online as well as in 2 different physics books that derive the relativity equations.
Just out of interest, what books did you use to study relativity? How firm an understanding of general relativity do you have?
My brother is currently majoring in physics in college for the second year, and my dad teaches Statistics and Calculus in highschool so I have a good deal of help at home. This is something that I really would like to learn about, so If you all recommend that I start with quantum field theory (having a confident understanding of relativity) than that is were I will begin. But, again, if this is what I should do, then links or ideas of where to start would be greatly appreciated, although I should be able to find help on that subject through google. Thanks.

I've not studied QFT yet (its my task for the summer!), so can't advise which books to use. There are plenty of people here who can though!

Well I have a grasp on relativity, not only was it well explained in "The elegant Universe", but I have done a lot of reading on it. online as well as in 2 different physics books that derive the relativity equations.
It's one thing to read a book that mentions the Einstein Equations, it's another to actually know how to do GR.

Have you done things like vector calculus and linear algebra? If not, then you simply don't have the mathematical tools to do GR properly. Similarly, you'd struggle to do QFT without doing quantum mechanics first and that usually requires linear algebra and vector calculus too.

An excellent QFT book is Peskin & Schroeder - An Introduction to Quantum Field Theory, but it does assume you're competent at non-relativistic quantum mechanics, Dirac notation and vector calculus.

Simply reading "The Elegant Universe" and flicking through a similar book on GR isn't enough to put you in a position to do the guts of string theory. You need to be very comfortable with a lot of calculus, linear algebra, group theory and then you can move onto doing the basics of GR and QM. After/during that you can then get into QFT and then onto string theory. There's a reason string theory isn't a typical undergrad course, because it takes a few years to teach physics or maths students enough for them to understand it.

What exactly is "vector" calculus. I've taken pre calculus and AP calculus courses. Is vector calculus concerned with derivatives and integrals to find slope and inflection points? Because if it is then we have gone over a lot of that. If not then I will start there. If yes then I will look over linear algebra and then I guess move on to general relativity?

To have an idea, read this....

http://www.phys.uu.nl/~thooft/theorist.html" [Broken]

... and good luck.

Christine

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Calculus is a word meaning roughly "deep analysis of a topic with concentration on performing calculations", or typically what and why you do math in a typical high school curriculum (except maybe for Geometry). A vector typically means an element of R^n (R^n means an n-dimensional "space" of the real numbers, such as a plane, a space, or a hyper-space (such as space-time, which is akin to R^4))

Vector calculus therefore is the study of topics needed to do calculations with vectors: addition of vectors, multiplication of vectors (dot product, cross product, scalar product, etc), vector functions, derivatives and integrals of vector functions, n-dimensional manifolds, etc.

You will not typically encounter these topics in an AP Calculus book because they are not necessary for the average, or even above average, high school student's knowledge of performing calculations. You will begin to cover the topics in a 3-Dimensional Calculus text, but you will need to study both Complex Calculus and Multi-Variate Calculus before you will have the sophistication with vector calculus needed for GR (and then you have a host of other topics that you must learn).

And sorry, but I'm a freshman in college, so I'm not nearly there yet.

Ok, I have a pretty good Idea of what I'm getting myself into. I didn't expect that I needed quite so much to learn string theory, but I'm not put off by it. Going through all that other stuff is actually a plus, and even though some of it I may have to hear again at college, I think it would be worth my time to learn. I'm going to start with the information provided by ccdantas' link and go from there.

Thank you ALL for your help.

I didn't expect that I needed quite so much to learn string theory
With the exception of a very small handful of universities in the world, string theory isn't something you'd learn (except in your free time) until you were doing your PhD, it requires that much preparation courses. Many universities don't even do GR in any serious way until the last term of 3rd year or even into the 4th year/masters. Same goes for QFT. That's not because unis muck around, they just have a lot of groundwork to cover before someone can seriously hope to do those topics in any more than a "Shut up and crunch numbers" manner.

LukeD's description of vector calculus pretty much covers it. It's working with differential equations, integrals etc in multiple dimension/variables as well as things like vectors, vector spaces, transformations on multidimensional spaces, complex (ie using imaginary numbers) multivariable calculus etc.

To give you an idea of the work involved, 'vector calculus' was a 1st year course for me. String theory was a 4th year option to those who were interested. GR was a 3rd year course and then done again but deeper in the 4th year. QFT was 4th year too.

I'm not trying to put you off, it's always good when someone is interested. I just don't want you to think it'll just be a matter of flicking through a calculus book and you're ready to go. Unless you're a genius (and even then!) it'll be a lot of work, but very rewarding if you keep it up :)

Ok, I have a pretty good Idea of what I'm getting myself into. I didn't expect that I needed quite so much to learn string theory, but I'm not put off by it. Going through all that other stuff is actually a plus, and even though some of it I may have to hear again at college, I think it would be worth my time to learn. I'm going to start with the information provided by ccdantas' link and go from there.

Thank you ALL for your help.

By all means, learn as much as you can. I'm currently considering Math as a major, and I wish that I had learned a lot more math when I was in high school instead of trying to teach myself Computer Science (which I realized a few years ago that I did not want to go in to). If you teach yourself properly, you can test out of some of the earlier classes (by taking AP tests and the such), and if you take college courses at local colleges, depending on which college/university you attend, you can get transfer credit and move to more advanced topics.

Also, keep in mind that Calculus is only a small subset of math. Math is not only about performing calculations; it's also about logically analyzing systems (in the broadest sense). If you are interested in physics and you like to teach yourself math, you may also find that you like the rigor of more formal mathematics. Furthermore, rigorous mathematics is constantly finding its way into physics in ways that often surprise less mathematically-inclined physicists because it has led to amazing insights and results that otherwise may not have been possible. For instance, Quantum Mechanics' later developments were made possible by Hermann Weyl's demonstration that it could be formulated in terms of a gauge theory.

I don't know much about string theory but I think that one also needs to have a good understanding of modern algebra and complex variables in order to understand string theory, am I right?

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Demystifier
Gold Member
To have an idea, read this....

http://www.phys.uu.nl/~thooft/theorist.html" [Broken]

... and good luck.

Christine
The most useful post so far!
In fact, I often recommend the web page of 't Hooft to the beginners in theoretical physics.

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