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Mastubara transform conventions

  1. Jul 9, 2011 #1

    When calculating the dynamic structure factor I need to express [tex]\rho(q)[/tex] in terms of creation and annihilation operators. I tried a direct calculation of the form

    [tex] \rho_q = \int e^{i q x} \bar{\psi}(x) \psi(x)[/tex]
    [tex] = \int e^{iqx} \sum_{k k'} e^{ikx} \bar{\psi}_k e^{-ik'x} \psi_{k'} [/tex]
    [tex] = \sum_k \bar{\psi}_k \psi_{k+q} [/tex]

    however in all of the literature the result is stated

    [tex]\rho_q = \sum_k \bar{\psi}_{k+q} \psi_k [/tex]

    I've thought of the following possible causes for this discrepancy:
    1. I'm using the wrong sign convention for the transform: WRONG because even if I switch all of the signs of the exponents we get back the same result.
    2. ONLY the sign of rho's exponent is wrong: possible, because it seems that it is arbitrary to decide that rho transforms like psi and not like psi bar.

    This is where I'm at. I would really like to understand the source of the mistake.

    Thanks for any help!!
  2. jcsd
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