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3-point function QFT

  1. Jun 2, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm working on path integrals for fermions and I came across an exercise that ask to compute the three point functions , one of that is the:
    $$<0|J^{\mu}(x_1)J^{\nu}(x_2)J^{\rho}(x_3)|0> $$
    where $$J^{\mu}$$ is the current $$J^{\mu}=\bar{\psi}\gamma^{\mu}\psi$$.

    ***Can you give me an idea or an example on how to compute this things?***

    Because I'm trying to use the usual logic about I don't see what I can do about the gammas isnside the correlation.

    The sourse functional for fermions is :
    $$Z[\eta,\bar{\eta}]=\exp\{-i\int dx\;dy\; \bar{\eta}(x)S(x-y)\eta(y)\}$$
    where $$S(x)=(i\gamma^{\mu}{\partial_{\mu}-m)^{-1}}$$.
     
  2. jcsd
  3. Jun 2, 2015 #2

    fzero

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    The correspondence between appearances of ##\psi(x)## and derivatives ##\delta/\delta \eta## is derived from the form of the source functional before the fermion field has been integrated out. You should be able to prove that the ##\gamma##s have to be inserted between the derivatives.
     
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