the preceding post is the best I could do as direct answer to P Tabor's question. he wanted to know what courses to take. I answered relative to non-string QG. Other people may have other ideas for him.
this next is just some general observations about QG which might be helpful. I couldn't decide to leave them or to erase the post.
QG is getting more "topological".
the practical meaning for you, if you are an undergraduate physics major, is that you should probably make sure you take a course that introduces DIFFERENTIAL FORMS and things like exterior derivative and wedge product.
It might be NICE to also take an introductory topology course in the math department but that may not actually do much for you (depending on the course) and personally I don't think it is essential.
the main thing would be to get some familiarity with the manifolds equipment of differential geometry and in particular with diff. forms.
If you are just doing a physics major then you may not get around to QG for some years, but when you do knowing some of this differential geometry will be a good investment.
For starters, one concrete suggestion might be to take some kind of advanced calculus/diff geom class where you learn about differential forms.
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if you are a self-taught person there are online resources like one comes to mind is called
Preparation for Gauge Theory someone in Brazil wrote. It is 100 pages and covers a lot.
But you said what classes, not what online resources.
are you at a university? (you mentioned taking classes)
do you have the math department catalog handy, or the general course catalog?
what is the lowest number math class that says "differential geometry"?
also BTW what is the lowest number math class that says "topology", and the lowest that says "algebraic topology"?
tell me what the name and coursdescription says, maybe I or somebody else can help figure out
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the old basis of physics was foursquare euclidean geometry called
Rn. it was built on that, and elaborations, in the 19 century----a fixed flat space with a fairly rigid notion of the natural coordinates to use and a few set transformations between them.
and then there is the 1905 liberation with special relativity which means moving to "Minkowski" space----still fixed and flat and with a narrowly defined class of kosher coordinates.
then in 1915 the GRAVITISTS split off and built their gravity spacetime physics with DIFFERENTIAL GEOMETRY which means you can use curved coordinates and there is no idea of right ones, and you can do a lot of it in a "coordinate-free" fashion which means that your notation POSTPONES the choice of coordinates. the shape of space becomes a dynamic variable along with the other dynamically varying quantities.
but practical working physicists like Jackson did not immediately follow the Gravitists off into the fabled realms of diffy geom. They kept on working with primitive rigid space like euclidean or Minkowskispace of special relativity. After all effective macroscopic real space IS nearly flat and Minkowski is nearly right if gravity is negligible. Minkowski space is what EMERGES when you turn all the interesting stuff off.
What makes today's situation hard for us (who want to watch and learn) is that the (quantum) Gravitists NOW SEEM TO WANT TO GO SOMEWHERE BEYOND DIFFERENTIAL GEOMETRY and it is not obvious what that will be. maybe the fundamental picture of space they find at micro level and ultimately build the rest of physics on will NOT BE A MANIFOLD (not be a differentiable manifold, the standard idea of flexible continuum) maybe it will be a mess of purely topological information without any decent coordinates at all.
maybe you can
abstract out all the topological relationships than can arise among things in a continuum and then
throw away the continuum
and maybe then, contrary to all reasonable expectations, you can
still do physics there
this would have conventional physicists tearing their hair out by handfuls and would be a big funny surprise to watch.
their familiar Minkowski space would be what emerges as the limit as you gradually turn the knobs and shut all the interesting stuff down.
and Minkowski space is what JACKSON ELECTRODYNAMICS IS BUILT ON so come to Papa baby.
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because we might NOT be in a gradual change situation but we could be in for a kind of rough JOLTING ride, maybe you should get a direct taste of what is going on. instead of my being able to tell you what courses to study, you maybe should look at some recent papers and try to guess for yourself. At least you get a taste of it now, which could gradually grow into insight later.
there is a baez paper with arxiv number "oh-fortyfortyforty" called "Quantum Quandaries"----F-H just mentioned it in that other thread----the Baez Perez thread. I would not have thought of it but F-H is probably right. he is doing his masters in this stuff right now and masters students usually know what to read.
Ah hah! that is what should happen. F-H should see this thread and suggest some things to you. If he wants, he could be much more helpful. My advice is keep on with jackson and do a standard Physics major and meanwhile just keep an eye on things.
sample arxiv links:
http://arxiv.org/find/gr-qc/1/au:+Baez_J/0/1/0/all/0/1
1. gr-qc/0605087 [abs, ps, pdf, other] :
Title: Quantization of strings and branes coupled to BF theory
Authors: John C. Baez, Alejandro Perez
Subj-class: General Relativity and Quantum Cosmology; Mathematical Physics
2. gr-qc/0603085 [abs, ps, pdf, other] :
Title: Exotic Statistics for Strings in 4d BF Theory
Authors: John C. Baez, Derek K. Wise, Alissa S. Crans
Comments: 41 pages, many figures. New version has minor corrections and clarifications, and some added references
Subj-class: General Relativity and Quantum Cosmology; Geometric Topology
3. quant-ph/0404040 [abs, ps, pdf, other] :
Title: Quantum Quandaries: a Category-Theoretic Perspective
Authors: John C. Baez
Comments: 21 pages, 2 encapsulated Postscript figures
Subj-class: Quantum Physics; Quantum Algebra
