I continue to read Sheldon Katz’s book “Enumerative Geometry and String Theory”. Here’s question I posted on sci.physics. If you have any answer, comment or ANYTHING, please (rather: I BEG YOU, CRYING ON THE FLOOR!!!) share them. It’s really hard to find someone who is mathematician and who’s interested enough in physics to answer even such simple questions… In my department there is only one more guy I didn’t yet ask (about what follows or some other physical questions) , but I don’t trust him – he was a physicist in his youth.

!Clarification update! I didn’t mean that if you’re physicist then I don’t want to see your comments – I do even more! It’s just that I have generally bad experience with talking about physics with physicists on my university. Especially with this guy I mentioned above, which was particularly dissapointing, ’cause he’s sort of both mathematician and physicist…

So here goes my post:

Yo,
I’m reading Sheldon Katz’s book “Enumerative geometry and string theory”, chapter 11. I know nothing about QFT or physics so please use polite language (for example, D-brane, string, SUSY are very impolite (unless [explained or given with reference] for dummies) while connection, Sobolev space, Poincare duality etc are honey for my ears).

SK says that we’ll be doing this QFT on (n+1) or (n+0) dimensional X, called spacetime; and that we’ll be interested in fields on X of mainly two types:
1) sections of vector bundles
2) maps from X to another manifold Y

First question: what physical meaning have fields of second type? I hope that fields of first type are old-school fields, like 4-form coming from Maxwell equations, etc. – am I right?

Second “question”: well, actually I know that unfortunately I’m not right, because SK gives following weird example: (0+1) dimensional X and fields are real-valued functions. He introduced Action Functional S(x(t)) = “here stands precisely the standard integral used for deriving Newton’s laws of motions)”. Why it’s weird for me? Because X is called “space-time” and here it isn’t space-time. Rather, on X there are fields which can be interpreted as functions from time to “real” spacetime. So it’s weird – is it normal? Should I abandon this nice idea that space-time in QFT roughly corresponds to real space-time?