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Group Theory-Help

  1. Jul 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Given the element:
    G(x,θ,θ*)= ei(xμpμ+θ Q+θ*Q*)
    Show that:
    G(0,ξ,ξ*) G(x,ζ,ζ*)= ei(x'μpμ+(ξ+ζ) Q+(ξ*+ζ*)Q*)

    and what does x'μ stand for?

    2. Relevant equations
    Some comutation formulas.
    [ξQ,ξ*Q*]=0
    [pμ, ξQ]= ξpμξ*

    3. The attempt at a solution
    I tried to use Baker Campbel Hausdorff formula several times, but I ended up failing to reach the wanted result.
    I am trying to show that
    exp[A] exp= exp[C] where A, B, C are the operators on the exp of G.
    and find C of A and B, right?
    from BCH we have that:

    eA+Be-[A,B]/2

    Now A+B term is very nice for me, because it creates the (ξ+θ)s I have... But does not ruin xμ.

    and the problem comes with that [A,B] which is not zero :(
    And it doesn't have to be because I am looking for a new x, x', which I don't know what it is....so there must be a term of it somehow appearing...
     
  2. jcsd
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