1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted