Complex scalar field propagator evaluation.by Ace10 Tags: compex, evaluation, field, greens function, klein gordon field, propagator, quantum field theory, scalar 

#1
Oct2913, 12:12 PM

P: 6

Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex KleinGordon field. Although the procedure is the one followed for the computation of the propagator of the real KG field, a problem comes up:
As known: <0T[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 KG 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. 



#2
Oct2913, 12:16 PM

P: 6

sorry about the equation faults, if something is not clear or needs correction, please let me know.




#3
Oct2913, 01:22 PM

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.




#4
Oct2913, 01:55 PM

P: 65

Complex scalar field propagator evaluation.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. 



#5
Oct3013, 06:58 AM

P: 6

I think its ok now..Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex KleinGordon field. Although the procedure is the one followed for the computation of the propagator of the real KG field, a problem comes up:
As known: <0Tφ + (x)φ(y) 0> = Θ(x 0 −y 0 ) <0φ + (x)φ(y) 0> + Θ(y 0 −x 0 ) <0φ(y)φ + (x) 0> and <0φ + (x)φ(y) 0>=<0φ(y)φ + (x) 0> But if we try to verify that one of the above correlation functions is a green's function of the KG equation we hit the obstacle: ∂ x <0φ + (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? 



#6
Oct3013, 07:14 AM

P: 976

See if this helps,you can see it further in Peskin and Schroeder's book.




#7
Oct3013, 08:40 AM

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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