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Complex scalar field propagator evaluation.

  1. Oct 29, 2013 #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. Oct 29, 2013 #2
    sorry about the equation faults, if something is not clear or needs correction, please let me know.
     
  4. Oct 29, 2013 #3

    Avodyne

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    Try putting the entire equation in tex. The tex symbols for left and right angle brackets are \langle and \rangle.
     
  5. Oct 29, 2013 #4
    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. Oct 30, 2013 #5
    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. Oct 30, 2013 #6
    See if this helps,you can see it further in Peskin and Schroeder's book.
     
  8. Oct 30, 2013 #7
    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.
     
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