### My first “PhD” e-mail…

22Apr08

Recently I activated my e-mail account for my PhD institution. This was a cause for minor celebration (while writing up one finds excuses for many minor celebrations). You hence can imagine that I was ready to put my fiesta-hat on when I received my first e-mail at this new account.

Unfortunately, this was the first line of the inaugural e-mail:

Crime alert: Incidents of stalking reported

Well, maybe I can celebrate my

*second*e-mail…Filed under: Just for Fun, Student Life | 6 Comments

Let me guess… you are going to Berkeley!

Btw, can you do a lit review of maths books for physics, especially what books you found useful for learning differential geometry and clifford algebras.

Hi Besu — I’m not sure if I’m qualified to give such a review since I haven’t really spent much time looking at what’s out there. I’ll give my quick thoughts, however.

A good starting point might be the Part III notes for “Differential Geometry for Physicists,” (http://www.damtp.cam.ac.uk/user/gr/about/members/gwglectures.html) and the references therein. You may have to tune that to be more or less formal depending on your tastes.

Most physicists learn differential geometry through GR, so perhaps Carroll’s book might be a good place to go if you want a physical introduction. (The appendices are very good for filling in mathematical details.) A much more idiosyncratic approach is Misner-Thorne-Wheeler. (I’m very curious about how much a clever high school student could learn with that book.)

Slighly more formal are the books by Frankel (Geometry of Physics) and Nakahara (Geometry, Topology, Physics). These tend to be more useful as reference books, I think, but you might find them useful. There’s a little book by Schutz on geometrical methods that’s also nice.

If you really want to see differential geometry in action, then Arnold’s Mathematical Methods of Classical Mechanics is rather good. (There’s also a big paperback book by Jose and Saletan with similar subject matter.)

My stringy friends seem to like a two-volume differential geometry text by an author whose last name starts with a ‘K’. (Um… the cover is black with white text and is part of a series of mathematical texts, if that helps?) Mathematicians also seem to like Spivak’s multivolume treatise (“the great American differential geometry texts”)… they have the benefit of having very cute cover art based on the Rime of the Ancient Mariner.

Since you’re especially interested in Clifford Algebras, I was recently pointed towards a two volume text by Choquet-Bruhat which seems to do a good treatment of these sorts of things.

Anyway, I hope that was helpful. Let me know how it goes!

besu, some friends and I went through a dozen books on Clifford Algebra and without a doubt the best treatment for a physicists is in Geometric Algebra for Physicists. It alternates between theory and a single application in physics, lays the groundwork with just enough rigor and more clarity than other books, and the application chapters (those which I could understand) clearly explain how to use the concepts in a dozen areas of theory.

Exciting first email fliptomato! The life of a physics PhD is more mad and dangerous than many suspect!

I’ll be doing physics at Berkeley next year, too… interestingly I haven’t gotten anything from them concerning activating an email account.

The two volume book you’re thinking of is Kobayashi and Nomizu…and frankly, as a math student, I find it to be a TERRIBLE book to learn from. It’s a reference, though. I did like Carroll though, that was my first introduction to anything beyond what a manifold is, and for that, I kind of like Lee’s “Introduction to Smooth Manifolds.” Doesn’t do much with metrics, but Carroll has what you’ll really want there to start out anyway.

Nope, he’s going to Cornell