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4 tensor integration notation

  1. Oct 24, 2012 #1

    I have been going round in circles trying to figure it out so I figured it would be quickest and easiest to just ask:

    What is the definition of: [tex] \int f(x) d^4 x [/tex]

    I first thought it was:

    [tex] =\int \int \int \int f(x) dx^1 dx^2 dx^3 dx^4 [/tex]

    but now I am starting to think it is:

    [tex] = \int f(x) dx^1 +\int f(x) dx^2 +\int f(x) dx^3 +\int f(x) dx^4 [/tex]

    Thanks for any help.
  2. jcsd
  3. Oct 24, 2012 #2


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    Of course it's the first one. It's an integral over a 4D space/manifold, your second equality makes no sense.
  4. Oct 25, 2012 #3
    In general a factor of √g is absent in the former expression ,the second is just weird.
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