Learn Differential Geometry: Books for Bachelor in Geometric Quantization

[Fgard]

I am taking my bachelor in geometric quantization but I have no real experience in differential geometry ( a part of my project is to learn that). So I find myself in need of some good books that cover that the basics and a bit more in depth about symplectic manifolds.

If you have any recommendations that would be greatly appreciated.

 

[Alex Gian]

A very interesting book, with a quite distinctive approach, is Sussman, Wisdom and Farr's "Functional Differential Geometry", also available free online at https://groups.csail.mit.edu/mac/users/gjs/6946/calculus-indexed.pdf

The different thing about this book is that it is supported by software examples throughout, which you can run on MIT-Scheme's "scmutils/mechanics" software to check your understanding.

I have just started it myself. You may find you need another text, too, with a more conventional approach, but this one is really fun. They have stated that a lot of their inspiration came from Spivak's approach in "Calculus on Manifolds", so this may be just what you want.

Incidentally, Sussman and Wisdom, with Mayer, have done another quite well-known book, "Structure and Interpretation of Classical Mechanics", which gives the same practical, unambiguous treatment to Lagrange, Hamilton and dynamics in general.

 

[Fgard]

Thanks for the tip. I will check out the book.

 

[Alex Gian]

Hi Fgard,
Once you've had a chance to have a good look at it, I'd appreciate your opinion/feedback.
Like I said, it's quite an unconventional approach, so you may need to get your head around their style a bit, but really cool once you get going.

ScmUtils is a bit of an albatross, but does work well once you set it up. I know that there are people working on porting it to more modern envirnmonents , so hopefully this approach will catch on in the future...