String Theory AP physics project

[Aznespina]

I have been given a project in my ap physics class where I am to explain how Bose-Fermi equivalence, tachyon, dilaton, green-schwarz anomaly cancellation and kahler manifolds relate with string theory. After an hour of research, I realized that I could not find even the slightest information on several of the terms. Can anyone here give me a brief summary of the terms to start with?

 

[Simon Bridge]

Welcome to PF;
I am reading "AP Physics" as equivalent to an introductory college course, so you are probably only required to know the concepts.

I think you want a volume called something like "introduction to string theory".
The concepts are all related to Green Schwarz Witten superstring theory
So start there.

You should have found definitions for "tachyon", "Green-Schwarz anomaly", and "kahler manifold" quite simply - there are Wikipedia pages for the terms even.

The trickier ones:

Bose-Fermi equivalence: this is an equivalence between classes of gas/particle.
Most of the hits you'll get will assume you know what it is - but you should be able to read between the lines for most of them. How are particles represented in strings.

Dilation: ... of what?
Watch for the term in string theory discussions and read between the lines.

Do not expect to find a page telling you exactly what you want to know in no uncertain terms.
You will usually have to read around a topic and stay alert to get answers.

 

[bhobba]

I have been given a project in my ap physics class where I am to explain how Bose-Fermi equivalence, tachyon, dilaton, green-schwarz anomaly cancellation and kahler manifolds relate with string theory. After an hour of research, I realized that I could not find even the slightest information on several of the terms. Can anyone here give me a brief summary of the terms to start with?

Mate - that could be a Phd thesis - or at least a masters thesis - not an AP project.

I have an honours degree in math, and have read extensively in QM, and know a bit of the detail of string theory, and I would not even attempt to undertake any of those topics as a project of any sort, but as something that would require extensive and serious study that would stretch my mathematics to its limit. To ask an AP student to do it - well is not what you would expect from someone at that level.

Go back and say you have been told these are all very advanced topics, requiring very advanced math so exactly how does he expect you to undertake it.

Hopefully he will confirm he only wants a lay view of it. That being the case the following would be a good place to start:
https://www.amazon.com/dp/0465028373/?tag=pfamazon01-20

Even then it would be no easy task - good luck.

Thanks
Bill

 

[Simon Bridge]

I agree.
Isn't AP Physics a course?
So it should have course materials?
I am kinda expecting that there is some reference that the person setting the project expects you to use.

 

[Aznespina]

Dilaton was not an error; my sheet specifically says Dilaton. And my project is to scour the internet about topics relevant to String Theory. It's not actually part of the core curriculum (just an end of the year post-AP test research project), and there have been nearly no hits about Bose-Fermi Equivalence besides research papers. Halp :/

 

[Simon Bridge]

Dilaton was not an error; my sheet specifically says Dilaton.

Never said it was. My comments are supposed to guide you to better searches.
You ca look up what the word "dilation" means in a dictionary, for example, but the key t figuring out what to look for is to figure out what the word applies to. What is the context? That is something you need to do yourself, and you won't get it until you've done some reading around the other topics.

And my project is to scour the internet about topics relevant to String Theory. It's not actually part of the core curriculum (just an end of the year post-AP test research project), and there have been nearly no hits about Bose-Fermi Equivalence besides research papers.

Since your project is to search for these things, actually giving you a link would amount to doing your work for you.

All I can do is tell you how to refine your search.
You've been provided with a link to an introduction to string theory, and a number of search terms to try. Have you tried those?

Don't expect to get hits for all the terms right at the start - read the information you have, it will provide clues to where to look for the rest. Getting you to do that is the whole point of this sort of exercise. It is not supposed to teach you string theory - that is beyond your level - it is supposed to teach you about information searches.

 

[ZapperZ]

And my project is to scour the internet about topics relevant to String Theory. It's not actually part of the core curriculum (just an end of the year post-AP test research project), and there have been nearly no hits about Bose-Fermi Equivalence besides research papers. Halp :/

And your instructor is OK with this? How are you to know if what you discover during your internet scouring is actually valid and not some crackpot ideas, or dubious, off-the-wall theories? What have you accomplished by doing such a thing?

Zz.

 

[Vanadium 50]

Simon, it's you who is making the mistake. It really is DilaTON and not DilaTION.

I agree with Zz. In addition, you have the problem of context. Without context - the context one gets only after many years of study - it's just words. It would be like trying to learn French from a French-English dictionary - with 3/4 of the pages ripped out.

 

[Simon Bridge]

Simon, it's you who is making the mistake. It really is DilaTON and not DilaTION.

... ah - and I did that multiple times too :(
But please note: I have not claimed that there was a mistake in post #1.

Anyway - discussions on how dilatons relate to string theory are very common just googling the word.
Shouldn't take hours to find them.

Checking: post #1 does say this specific project was given to OP in this form.
The only legit teaching reason I can think of for this sort of project to be deliberately supplied at this level is as a way of making students work at searching for information.

Yeah students will need to do some vetting.
I also expect that the project setter does not expect students to be able to write comprehensively on all of the listed items unless there is a specific source in mind.

But I'm not there.
Maybe the topic was chosen by OP after all, or maybe the teacher is being over-optimistic?

 

[bhobba]

And your instructor is OK with this? How are you to know if what you discover during your internet scouring is actually valid and not some crackpot ideas, or dubious, off-the-wall theories? What have you accomplished by doing such a thing

Exactly. The validity of stuff you read in physics lies in being able work bough the concepts and math to check what is being said. At AP level your background is woefully inadequate for that task with those topics. Even as a graduate, unless you had specialist graduate school training, those topics would still likely be, to put it mildly, well mathematicians have a term for it, highly non trivial, meaning it's HARD

Thanks
Bill

 

[ChrisVer]

Hello.
Apart from trying to find a relation of them with the Strings theory, you should first come to understand what each term is all about. Do you? What is a Kahler Manifold for an example, or what are the tachyons and dilatons, or how they appear in the String Theory formalism?
If you haven't looked deeply (by that I mean, doing some calculations on your own, doing mistakes or finding the correct answers) I don't understand how you could get a paper on those fields and study it... leave aside presenting it.
But nevertheless, that's a problem of your supervisor who gave you such a project...Probably you should ask for some guidance - he'll know better which reference will suit you best, since you are his student. But before you do, make some research on yourself on those terms one by one, so that you can speak in the same language...
There are indeed papers looking into Kahler Manifolds assosiated with ST:
http://arxiv.org/pdf/1305.4838.pdf
maybe in the references you might find something more interesting to you

For tachyons at least for the (bosonic) string theory, you can have a look at Zwiebach's book... it's for an introduction level.
For the statistics (if that's what you mean by Bose-Fermi equivalence) of String Theory, you'll probably be able to find on your own. Zwiebach for sure has a chapter about the statistics of Black Holes, and also there are the book's references to look at. Also there have been some papers around dealing with the partition function for string models. If on the other hand you meant Bose-Fermi equivalence as the number of bosonic degrees of freedom= fermionic, then you should also have a look at the superstring theory.

Dilatons I don't know- but I suppose you'll find easily.

For the G-S anomaly cancellation, I don't know either. But why don't you have a look in Schwarz's book on String and M theory?

 

[mitchell porter]

"Bose-Fermi equivalence" is the odd one out in that list. All the others are core topics in string theory: the tachyon and dilaton are particular states of the string, the anomaly cancellation was the discovery that made string theory popular in 1984, the extra dimensions are often assumed to be a Kahler manifold. But Bose-Fermi equivalence is a bit obscure. Maybe whoever made that list of topics was thinking of supersymmetry?

 

[Aznespina]

"Bose-Fermi equivalence" is the odd one out in that list. All the others are core topics in string theory: the tachyon and dilaton are particular states of the string, the anomaly cancellation was the discovery that made string theory popular in 1984, the extra dimensions are often assumed to be a Kahler manifold. But Bose-Fermi equivalence is a bit obscure. Maybe whoever made that list of topics was thinking of supersymmetry?

After some more research, I have a general understanding for all of the terms except "Bose-Fermi equivalence". I asked my teacher and she assured me that "Bose-Fermi equivalence" could be found with a simple google search. However, when I type it into google, I can only find research papers that I find completely impossible to understand. Does anyone here know if it can be found, or should I ask my teacher again? This project has never been done before by my teacher;my class is essentially her "guinea pig" for this assignment.

 

[Haelfix]

Your teacher is probably thinking of something else but has bungled her language. The term Fermi-Bose equivalence is not standard and ambiguous.

Ask her if she is referring to a concept related to supersymmetry or if she is referring to a special duality between theories.

In either case this is likely well over the head of a high school student, and even a Wikipedia like understanding of the answer is going to necessitate a long precursor chain.. Too much really.. Ditto with the GS anomaly cancelation mechanism and Kahler manifolds (she is probably thinking specifically about Calabi Yau spaces, which are an example of a Kahler manifold). Except that it's easier to write about CY spaces in such a context and gloss over the hard mathematics whereas defining what is Kahler requires getting into complex analysis and differential geometry.