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Zwiebach's A First Course in String Theory

  1. Oct 6, 2007 #1
    What mathematics and physics do you need to know to work out of Zwiebach's A First Course in String Theory?

    This is what i think i need to know;

    1st year calculus
    1st year linear algebra
    1st year physics (Mechanics, Electromag, Vibrations..)

    2nd year "Advanced engineering mathematics"
    2nd year Analysis
    2nd year Differential Equations
    2nd year Linear Algebra
    2nd year Calculus
    2nd year physics (Statistical, Electro, Quantum)

    3rd year Algebra
    3rd year Relativity

    Is there any other mathematics or physics that I have to know, do i have to know topology, tensor calculus/differential geometry??

    I really need to know :S

    I would value and appreciate all comments
    Last edited: Oct 6, 2007
  2. jcsd
  3. Oct 6, 2007 #2
    Also, could i use "A First Course in String theory" hand in hand with "String Theory and M-Theory: A Modern Introduction" or is "String Theory and M-Theory: A Modern Introduction" to harder text or does it involve differential geometry

    Thanks, Kurt
  4. Oct 7, 2007 #3

    Zwiebach's book is pretty self-contained. I would say that you need a solid background in undergrad physics (i.e. Griffiths QM and EM). Other than that, he goes through most of the math that you need. You don't NEED relativity, but it will help you in the book.

    I would make sure I understood all of Zwiebach's book first, then start with Becker Becker and Schwartz. Most of the math you need will be taught in the book---in order to start doing calculations, you only need a cursory understanding of the maths. The more important thing that you should learn before going through the Becker Becker and Schwartz book is Quantum Field Theory. I really feel like QFT is absolutely essential to understand string theory---this is how the theory was first developed, and to read any of the canonical text books (GSW or Polchinski), you really need to understand such things as BRST invariance and path integrals.
  5. Oct 7, 2007 #4
    Thankyou Ben, if i may presume this. What is the best, "advanced", Vector Calculus text book for 2nd year Uni. And might i ask, when in Uni do you get to learn about yang-mills theory?

    Also what is BRST invariance?

    Thanks for the help
    Last edited: Oct 7, 2007
  6. Oct 7, 2007 #5
    I would add a suggestion.

    Betwen the Zweibach book and the becker-becker-schwarz I think it would be a good idea to read the michel Dine´s "supersymmetry and string theory". Sure, it is not a bookd to get a deep knowledege of string theory, but it could serve as a way to get an overview presentetion of key ideas withouth going over the details. This can advoid that someone get losed with teh details and wouldn´t see the whole picture. B.T.W. You can read the stringy part of Dines book without previously reading the first chapters (I have done it) althought I guess that it is very interesting to read also the other chapters (but I haven´t still done it, so I can´say for sure).

    Also I would recomend the lecture of the second volume of Polchinsky book (and the necessary material from the firs one) to somewhat complement the becker-becker-schwartz.

    To end up discusing the standard books, Ben, could you tell me your opinion on "D-Branes" from Clifford Jonshon (if you have readed it). I have had to read it twice to understand many aspects of it. And in fact I guess that if I have undesrstood it is because I had readed the stuff (Or part of it ) on another sources. Be sure that I wouldnt recomend it as the best way to get used with string theory.

    B.T.W. I really liked the Michio Kaku books. It is a pity that now they are somewhat outdated, and that the part on M-Theory/branes on the "string theoroy and M-theory" is too short. I still think that are the more elegannt books on the subject.
    Last edited: Oct 7, 2007
  7. Oct 7, 2007 #6
    Yes Sauron, I also like the michio kaku books as well, my personal favorite one is Hyperspace, but if you are referring to his more advanced textbooks like "Introduction to Superstrings and M-Theory" or "Quantum Field Theory: A Modern Introduction" then i cant comment.

    There is just one thing, do u reckon that i will get lost in the maths of Zwiebachs book?

    (the maths i intend to do/done is in my first post)
  8. Oct 8, 2007 #7
    Yes I was refering to the most advanced books, I didn´t read the divulgative ones, but the question was mainly intended for Benthemen.

    About your skills in math/physics I hope they will be enought for at least understanding most of the subjects (hope your course of quantum mechanics would have been good anyway).

    But in these days you always can give a try to wikipedia whenever you get lost at some specific point. It is not a way to get a professional in a field, but for sure it is fine to help in a hurry-up.
  9. Oct 8, 2007 #8

    You will probably not learn about Yang-Mills theory for a long time. It is generally reserved for the third semester of a three semester class on QFT, which you will take in graduate school. I pretty much had to teach myself about Yang-Mills. This is why you should stick to Zwiebach's book for the time being, and learn the fundamentals very well.

    Stick to your undergraduate classes for now. Learn QM and EM and classical mechanics, and stick to your maths. About math books, I never could learn very much from them. Take the classes that your school offers on complex analysis, differential equations, and calculus.

    I could never learn anything from one book, so I own most of the string theory text books. My research is mainly focused on older heterotic string theory, so the first volume of GSW that I own is pretty well-worn. That said, the DBranes book is pretty good, but only as a complement to the GSW and Polchinski, none of which you can learn ANYthing from unless you know QFT up and down.

    I got through about half of Cliff Johnson's book before I quit and started reading more supersymmetry.
  10. Oct 12, 2007 #9
    What do mathematical terms such orientifolds, hitchin functionals, 6-manifolds, compactifications, half-flat manifolds, NS-NS B-fields and NS-NS fluxes mean? What mathematics do i have to know before i can understand string theory or read string theory research papers in journals?
  11. Oct 12, 2007 #10
    There is a pretty steep learning curve when you first start learning any field. You should know quantum field theory very well (the best string theorists started out as quantum field theorists), and then go through Green, Schwartz and Witten or Polchinski. You'll learn all of the relevant maths you need in those books, usually. Most of the rest of the stuff you can pick up as you go along. For example, I don't know what an orientifold or a hitchin funftional is.
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