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Quaternion and Pauli matrix

  1. Sep 2, 2005 #1
    i am learning Quaternion now for my EM course. Can someone enlighten me on the correspondence between Quaternion and Pauli Matrix algebra?
     
  2. jcsd
  3. Sep 2, 2005 #2
    Not so easy to explain;
    metric tensor of the Minkowski's space <=> introduction of the quaternions;
    a proposition from Dirac to discuss the Schrödinger equation => introduction of (4-4) matrices built in fine with the (2-2) Pauli's matrices;
    Let us call m(a) for a = 0, 1, 2, 3 the different (4-4) matrices; the discussion shows that following relation must hold: m(a). m(b) + m(b). m(a) = 2. g(ab)
    where g(ab) is the metric tensor for a Minkowski’s space.

    So: not a real good explanation (sorry) but a short exposé of the connections between the actors
     
  4. Sep 2, 2005 #3

    selfAdjoint

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    From this site: http://home.pcisys.net/~bestwork.1/HamiltonQ/hamilton.htm

    This quote:
     
  5. Sep 3, 2005 #4
    still yet to figure out.. but the web link looks pretty informative. Thanks. Will see if i can make some sense out of it.
     
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