Looking for notes on guage geometry.

[Haelfix]

Hi, I was wondering if there was anyone who would have a good set of lecture notes online concerning the following problem

Basically, what I am looking for is the construction of the classical lagrangian of general relativity + classical Yang Mills fields using differential geometry, bundles, gauge connections etc. But not really.

I am really more interested in the way to go from the classical theory to the quantum field one, using this language. I am trying to stay away from the Palatini formalism, where they abstract away from the Einstein Hilbert action and use SO(3,1) as the connection variable.

I'm tired of translating the usual way we are taught quantum field theory, into this language, and I need a good review set of notes that isn't scattered around in various tomes.

Any help or suggestions would be greatly appreciated.

 

[marcus]

... classical Yang Mills fields using differential geometry, bundles, gauge connections etc...

this is more elementary than what you are asking about----a preparation that introduces concepts of differential geometry: bundles, connections etc..

http://arxiv.org/math-ph/9902027

George Svetlichny
Preparation for Gauge Theory

the Yang-Mills lagrangian is introduced on page 61 (equation 89)
the Dirac operator on page 85

the notes are only 97 pages
I'm curious as to whether you know them and, if so, how you like them.
the style impresses me as unusually clear and efficient
maybe what you are looking for would be like a continuation of
these notes focusing on gravity?

 

[Haelfix]

Yea those notes are pretty good, I particularly like the bits on clifford algebras, as they are fairly readable. The reference text for that sort of thing is Nakahara (sp)

Essentially what I would be looking for, is part2 of those notes, generally speaking.

Everything there is semi classical, and I'm interested in the quantization procedures and treatment thereof using that language.

After googling for a little while, one invariably ends up getting texts on noncommutative algebras, which is a little abrupt for me. I'd rather that topic be introduced in the last 10 pages or so of the hypothetical text, and the QFT be walked through a little slower (for those like me who are a little light on grey matter and can't instantly absorb the full notation without a little bit of prep work).

 

[marcus]

...Essentially what I would be looking for, is part2 of those notes, generally speaking.

a Part 2 of Svetlichny's notes is an appealing idea
one wants to email him and say "Well? do you have Part 2
in the works?"

the concepts are elegant and the exposition graceful and efficient

hopefully you will find something that will serve, if so and it is online
please post