String Theory: Recommended Sites & Math Background

[physicsisphirst]

my son and i are just learning string theory.

i was wondering whether there were any recommended websites other than the elegant universe (we have found a couple and they are quite suitable, but we don't know enough to determine if there are preferred sites to go to).

also, what sort of math background should we be working towards? calculus, diff eqns i figure is needed, but the official site talks about K-theory and Noncommutative geometry which i don't have a clue about, but i guess this stuff isn't needed till one is well into things.

so any recommended game plans would be appreciated.

in friendship,
prad

 

[Imparcticle]

aloha, prad!

This site is helpful : www.stringtheory.com

 

[selfAdjoint]

aloha, prad!

This site is helpful : www.stringtheory.com

Did you mean www.superstringtheory.com?

 

[Javier]

Superstringtheory.com has a good description of the things you would need for a fair to full blown study of the theory.
I would be unsatisfied with Brian Greene's account as well, but that's because to really understand *why* the theory is studied and why it says the things it says, you ultimately have to come to the details, as I assume you have found.
Technical review articles on string theory can be found online (be careful what you choose, though). For example, http://xxx.lanl.gov/abs/hep-th/0007170 is a good place to check out the ideas involved in quantizing strings...you don't have to worry about the D-brane details here. Also, *section 2* of Polchinski's lectures is good: http://xxx.lanl.gov/abs/hep-th/9411028... the stuff on conformal field theories, matrix models, etc.
K-theory and non-commutative geometry are absolutely not necessary for an understanding of what the theory is about. Unfortunately, to go beyond the dogma in popular accounts, you do need a background in Lagrangian mechaincs, quantum mechanics, special relativity, a touch of general relativity (and preferably quantum field theory)...the mathematics for a basic understanding can be picked up through a study of physics. As for mathematics, interesting things in string theory are ultimately described using differential geometry, algebraic geometry, topology, algebraic topology...but you don't need all of this mathematics to get a next approximation to what the theory is about. It *is* important to know what physics came before the suggestion of string theory came about.
Good luck finding what you're looking for!

 

[physicsisphirst]

Good luck finding what you're looking for!

thank you, javier (and others)!
your post is very helpful because it puts things in proper perspective from which we can build a roadmap.

the point about learning what came before string theory is most significant too, because too often we try to learn only what we have to (before exams :D) without putting things into proper historical or logical context.

I have some questions that may possibly be a topic for a separate thread, but i thought i might as well ask it here for starters:

what happens to intuitive understanding in physics as we become more dependent on mathematics?
much of classical physics can be strongly intuitive, because we can see and feel what we are studying. when we probe the quantum world or explore say strings, we need the mathematics to provide the 'lab' since we really can't 'be there' to see what is happening.
does this mean that our intuitive senses gradually become irrelevant?

in friendship,
prad

 

[Haelfix]

To get beyond the layman view of string theory, D = 2 conformal field theory is absolutely essential. B/c let's face it, the layman view of String theory is pretty much nonsensical (at least it was to me when I first saw it)

The little understanding I have of rigorous string theory comes from this duality between conformal field theories.. And its just the first step elementary step in what seems to be one of the broadest and most challenging assortment of ideas in Physics.

Its not so far off from Nuclear physics really in that sense. A mismatched collection of ideas and models, that each are as varied, deep and dense as entire tomes of say fluid mechanics.

But seriously, I might advise against pursuing string theory as a layman. Its just going to confuse and bewilder, and it will look like nothing more than religion without the proper background material (which is already enough for about say 4 years of undergrad + 2 years of theoretical physics grad work).

As far as physical intuition goes. Well, keep in mind the intuition of someone who has been working in physics for a long time, is completely different from that same person before he started studying. We get used to thinking about things in a certain way, and the mathematical structure leads to its own sort of intuition.

One day, when the theory is fully flushed out and understood by the experts, I suspect it will be somewhat easier to teach to the layperson, but its still helter skelter atm, and probably will be for awhile to come.

 

[marcus]

what math to work towards

my son and i are just learning string theory.

i was wondering whether there were any recommended websites ...

also, what sort of math background should we be working towards? calculus, diff eqns i figure is needed,...

You asked about what math targets to steer for.

In a sense the first math one needs to get handy with, no matter what physics you want eventually to learn,
is the math required to do a good job with Freshman-level General Physics

You and your son may already have command of that, so my advice may be useless or inapproapriate for you.

But if you arent already up on that then maybe I can say that IMHO
the test of whether some math is indispensable or not is whether or not
you need it to do Freshman Physics-----that goes for calculus, differential equations, linear algebra, trig, geometry, a little complex variable maybe.

You will find that only rudimentary knowledge of, say, differential equations, will get you thru Physics 1A. But you need at least that much.

So my answer would be "whatever math is needed in standard for-first-year-science-majors College Physics!" (unless you and son have that already)
this is, I'm afraid, only vague and general purpose advice---it is not specific to one particular physics theory like string theory, it applies very broadly.

Common physics textbooks used to be Halliday Resnick
(now I think Jearl Walker is a sometimes co-author)
and another one was
by Douglas Giancoli
of course Feynman also did a fresh/soph physics text but its hard

the textbooks of choice may have changed.
but what's two years out of date might be available free from the library
while what is the latest edition favorite might cost plenty bucks to buy.

 

[physicsisphirst]

thank you haelfix for that very informative post. what you say about intuition of a physicist makes a lot of sense. knowing and using the math, certainly should not diminish or make one's intuition 'rusty' :D

thank you marcus. the subjects you mention are certainly what we are working towards. we have both haliday-resnick, feynmann, as well as a variety of math texts to follow these areas.

i think we will be busy for the next year :D

the comments have been most helpful so far and what i will do is post the path we take here so that it may be of some use to others as well.

in friendship,
prad