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4 dimensional curl as antisymmetric matrix

  1. May 5, 2012 #1
    I'm a bit confused. I'm trying to calculate the curl of a 4 dimensional matrix. It's an attempt to use stokes theorem for 4 dimensions.

    The curl can be written as a antisymmetric matrix from what I understand with entries,

    Mi,j = d Ai/d j - dAj/di

    where i and j would be the different coordinates like x, y, z etc... However, from what I understood if you looked the integral about an infinitesimal square in the x-y plane you could work out the integral as:
    (dAy/d x - dAx/dy)ΔxΔy

    I was informed that this would gives M1,2 ΔxΔy
    which would be wrong, you would get -M12 surely?

    So how does the curl look in matrix/ tensor form for 4 dimensions?
    Hopefully this makes some sense, sorry if it's a slightly confused question.
  2. jcsd
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