# Complex scalar field propagator evaluation.

by Ace10
Tags: compex, evaluation, field, greens function, klein gordon field, propagator, quantum field theory, scalar
 P: 6 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$\varphi^{+}(x)\varphi(y)$|0> = $\Theta(x^{0}-y^{0})$<0|$\varphi^{+}(x)\varphi(y)$|0> + $\Theta(y^{0}-x^{0})$<0|$\varphi(y)\varphi^{+}(x)$|0> and <0|$\varphi^{+}(x)\varphi(y)$|0>=<0|$\varphi(y)\varphi^{+}(x)$|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: $\partial_{x}$<0|$\varphi^{+}(x)\varphi(y)$|0> . And I refer to it as an obstacle because of the commutation relation [$\varphi(x),\pi^{+}(y)$]=0..How could i deal with this calculation..? Thanks in advance.
 P: 6 sorry about the equation faults, if something is not clear or needs correction, please let me know.
 Sci Advisor P: 1,185 Try putting the entire equation in tex. The tex symbols for left and right angle brackets are \langle and \rangle.
P: 65

## Complex scalar field propagator evaluation.

 Quote by Ace10 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$\varphi^{+}(x)\varphi(y)$|0>=$\Theta(x^{0}-y^{0})<0|$\varphi^{+}(x)\varphi(y)|0>+$\Theta(y^{0}-x^{0})<0|\varphi(y)\varphi^{+}(x)$|0> and <0|[/itex]\varphi^{+}(x)\varphi(y)|0>=<0|\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: $\partial_{x}$<0|[/itex]\varphi^{+}(x)\varphi(y)|0> . And I refer to it as an obstacle because of the commutation relation [\varphi(x),\pi^{+}(y)]=0..How could i deal with this calculation..? Thanks in advance.
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.
 P: 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?
 P: 976 See if this helps,you can see it further in Peskin and Schroeder's book.
 P: 6 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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