Compute 3-Point Function QFT Homework with Fermions

[nikosbak]

Homework Statement

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 $$S(x)=(i\gamma^{\mu}{\partial_{\mu}-m)^{-1}}$$.

 

[fzero]

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.