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Differential Geometry for General Relativity and Yang-Mills Theories

  1. Mar 11, 2014 #1
    I have been teaching myself QFT and General Relativity. The mathematics of those fields is daunting, and I find that what I have come across is very difficult to master. Of course it will take work, but can someone recommend a good text for self-leaning differential geometry with application to QFTs (particularly non-abelian guage theories) and GR? One that is clearly written and accessible to an amateur like myself. Thank you in advance.
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  3. Mar 11, 2014 #2
    I would recommend Elementary Differential Geometry by Pressley as a primer to differential geometry. And maybe supplement it with Differential Geometry by Kreyszig.
  4. Mar 11, 2014 #3


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  5. Mar 11, 2014 #4
    I like O'Neill for the basics of differential geometry of surfaces, which is the easiest place to start.
  6. Mar 11, 2014 #5


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    I think the best place to learn the basics of differential geometry has to be the books by Lee. They are close to perfect. Isham's book is a good place to get an introduction to the stuff that you need for gauge theories (but not the stuff you need for GR). If I remember correctly, it's not entirely rigorous, and it doesn't go deep enough, but it's a good place to start.

    Those are the books I have actually studied. If you want to go deeper, I think Fecko looks very interesting, and so does Frankel. But I haven't actually read them.

    John M. Lee: Introduction to smooth manifolds
    John M. Lee: Riemannian manifolds: an introduction to curvature
    Isham: Modern differential geometry for physicists
    Fecko: Differential geometry and Lie groups for physicists
    Frankel: The geometry of physics: an introduction
  7. Mar 11, 2014 #6


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  8. Mar 11, 2014 #7
    I have Frankel's text. I flipped through it to skim certain material; my general impression: if you can gain insight from just mathematical expressions , then it is great. I like a little more exposition myself. It is a better reference text once one has learned from a more accessible text.
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