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Grassmann Variables

  1. Feb 21, 2010 #1
    Can anyone advise on the following :

    Complete the square for this expression :

    (theta)*i Bij (theta)j +(theta)*i(eta)i +(eta)*i(theta)i

    where theta and eta are Grassmann variables and Bij an NxN matrix
    with indices i,j=1,...,N.

    Many thanks
    Last edited: Feb 21, 2010
  2. jcsd
  3. Feb 21, 2010 #2
    You can use limited latex in here if you enclose it in tex and /tex tags. Can you try to re-frame your question?
  4. Feb 22, 2010 #3
    In "componentless" notation, your expression is (?):

    A := \theta^* B \theta + \theta^* \cdot \eta + \eta^* \cdot \theta

    How about?:

    A = (\theta^* + \eta^* B^{-1}) B (\theta + B^{-1}\eta) - \eta^*B^{-1}\eta

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