Complex scalar field propagator evaluation.

  1. Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex Klein-Gordon field. Although the procedure is the one followed for the computation of the propagator of the real K-G field, a problem comes up:

    As known: <0|T[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> = [itex]\Theta(x^{0}-y^{0})[/itex]<0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> + [itex]\Theta(y^{0}-x^{0})[/itex]<0|[itex]\varphi(y)\varphi^{+}(x)[/itex]|0>

    and <0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0>=<0|[itex]\varphi(y)\varphi^{+}(x)[/itex]|0>

    But if we try to verify that one of the above correlation functions is a green's function of the K-G equation we hit the obstacle: [itex]\partial_{x}[/itex]<0|[itex]\varphi^{+}(x)\varphi(y)[/itex]|0> . And I refer to it as an obstacle because of the commutation relation [[itex]\varphi(x),\pi^{+}(y)[/itex]]=0..How could i deal with this calculation..? Thanks in advance.
     
    Last edited by a moderator: Oct 29, 2013
  2. jcsd
  3. sorry about the equation faults, if something is not clear or needs correction, please let me know.
     
  4. Avodyne

    Avodyne 1,276
    Science Advisor

    Try putting the entire equation in tex. The tex symbols for left and right angle brackets are \langle and \rangle.
     
  5. Hello,

    You should take a look at this link. I know it's quite hard to find, but it gives a pretty good introduction on mathjax/latex.
     
  6. I think its ok now..Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex Klein-Gordon field. Although the procedure is the one followed for the computation of the propagator of the real K-G field, a problem comes up:

    As known: <0|Tφ + (x)φ(y) |0> = Θ(x 0 −y 0 ) <0|φ + (x)φ(y) |0> + Θ(y 0 −x 0 ) <0|φ(y)φ + (x) |0>

    and <0|φ + (x)φ(y) |0>=<0|φ(y)φ + (x) |0>

    But if we try to verify that one of the above correlation functions is a green's function of the K-G equation we hit the obstacle: ∂ x <0|φ + (x)φ(y) |0> . And I refer to it as an obstacle because of the commutation relation [φ(x),π + (y) ]=0..How could i deal with this calculation..? Thanks in advance.
    As for the problem itself, any help?
     
  7. See if this helps,you can see it further in Peskin and Schroeder's book.
     
  8. Thanks adrien,I have in mind the corresponding paragraph in Peskin and Schroeder's book but I'll check this out too, it's quite helpful.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted