Differential Geometry for General Relativity and Yang-Mills Theories

[boltzman1969]

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 gauge theories) and GR? One that is clearly written and accessible to an amateur like myself. Thank you in advance.

 

[xiavatar]

I would recommend Elementary Differential Geometry by Pressley as a primer to differential geometry. And maybe supplement it with Differential Geometry by Kreyszig.

 

[dextercioby]

Well, I'd go for Mikio Nakahara's book. https://www.amazon.com/dp/0750306068/?tag=pfamazon01-20

 

[homeomorphic]

I like O'Neill for the basics of differential geometry of surfaces, which is the easiest place to start.

 

[Fredrik]

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

 

[WannabeNewton]

https://www.amazon.com/dp/9810220340/?tag=pfamazon01-20

 

[JaredEBland]

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.