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Integrating with volume element (d^3)x

  1. Aug 12, 2007 #1
    i'm at a loss about how to do this type of integration. can some one show me how to evaluate the integral of (d^3)k exp[ik*(x1-x2)]/[(k^2+m^2)(2pi)^3], where "*" is the dot product between the 3 vector k and (x1-x2), which are both 3 vectors. this come from the energy equation used to get the inverse square law (1/r^2).
  2. jcsd
  3. Aug 12, 2007 #2


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    The notation d^3x is usually shorthand for a volume integral with differential elements dx, dy, dz (In Cartesian coordinates.) So:

    [tex]\int_V f(x,y,z) d^3x = \int\int\int f(x,y,z) dxdydz [/tex]

    So, in your case, [tex]d^3k[/tex] probably stands for [tex]dk_x dk_y dk_z[/tex], where k_x, etc. are the components of the k vector. (Again, in Cartesian Coordinates)
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