Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Propagator for matrix fields (based on Srednicki ch80, p490)

  1. Nov 16, 2011 #1
    Hi,

    If I have a matrix valued field [itex] B(x)_i^{..j}=B^a (x) (T^a)_i^{..j} [/itex] and the relevant part of my Lagrangian is [itex]L=Tr(-\tfrac{1}{2}\partial^{\mu}B\partial_{\mu}B+..) [/itex] then how can I see that the propagator for the matrix field is [itex] \Delta_{i..k}^{..j..l}(k^2)=\tfrac{(T^a)_i^j(T^a)_k^l}{k^2-i\epsilon} [/itex] ?

    I understand that if we expand the L in terms of the coefficent field we get [itex] L=-\tfrac{1}{2}\partial^{\mu}B^a\partial_{\mu}B^{a} [/itex] and this leads to the propagator for the coefficient field as [itex] \Delta^{ab}(k^2)=\tfrac{\delta^{ab}}{k^2-i\epsilon} [/itex], (just like usual for a massless scalar field) but not sure how to see the propagator of matrix field...

    thanks for any help...
     
  2. jcsd
  3. Nov 18, 2011 #2
    Also why exactly does each external propagator carry at [itex] T^{a_i} [/itex] factor?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook