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Good resources for integrals in Four-Space?

  1. Nov 9, 2011 #1
    I've been looking for some good resources on integrals in four-space (SR and GR), and hope someone can suggest some! I'm not too interested in abstract mathematical formalisms to the extent of pure math though, I must keep in mind that this is all to do with physics (at least for me!).

    I know there are 4 kinds of integrals one can do in four-space:

    (1) Integrate a line element, ie. a curve.
    (2) Surface integral on a 2-D surface.
    (3) Integral on a 3-D hypersurface.
    (4) 4-D volume integral.

    Landau-Lifgarbagez gives a brief intro in their field theory book but I'd like to clear some things up instead of just having formulae presented to me.

    Any suggestions???

    Cheers guys!!
     
  2. jcsd
  3. Nov 10, 2011 #2
    Could anyone even tell me what area of math these fall under? Including such things as generalizations of Stokes and Gauss' theorems to hifger dimensions.
     
  4. Nov 10, 2011 #3

    Ben Niehoff

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    You should read about differential forms, but you have voiced a non-interest in "mathematical formalism", so you may well be stuck.
     
  5. Nov 10, 2011 #4

    George Jones

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    For general relativity, I think some of what you want is in sections 3.1, 3.2, and 3.3 from Eric Poisson's notes,

    http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

    which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of black hole Mechanics.
     
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