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Time ordering operator

  1. Jun 4, 2007 #1
    As I understand it, the time ordering operator works as follows (for [tex]t<0[/tex]):
    [tex]T c^\dagger(t) c(0) = -c(0) c^\dagger(t)[/tex] for fermions and
    [tex]T c^\dagger(t) c(0) = c(0) c^\dagger(t)[/tex] for bosons.

    Now suppose instead of these creation/annihilation operators, I had a more general commutation relation, ie [tex][d,d^\dagger] = S[/tex], how does the time ordering operator behave?

    Edit: After rereading that, I should be more specific. I'm trying to formulate DMFT equations in a non-orthogonal basis. So the creation/annihilation operators anti-commute to give [d_a,d_b^\dagger]_+ = S_{a,b}. The Green's function is usually defined as [tex]G(\tau) = \langle T c(\tau) c^\dagger(0) \rangle[/tex] and I need to understand exactly what the time ordering operator does, but I'm not even totally sure how its really defined, because as I understand it above, it works differently for fermions and bosons.
    Last edited: Jun 4, 2007
  2. jcsd
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