Register to reply 
Complex scalar field propagator evaluation.by Ace10
Tags: compex, evaluation, field, greens function, klein gordon field, propagator, quantum field theory, scalar 
Share this thread: 
#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: 1,200

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: 64

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: 1,020

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.



Register to reply 
Related Discussions  
Lorentz Invariance of Propagator for Complex Scalar Field  Advanced Physics Homework  4  
Complex scalar field propagator  Advanced Physics Homework  0  
Complex Scalar Field  Advanced Physics Homework  0  
Complex Scalar Field and Probability...Field  Quantum Physics  2  
Complex scalar field  Quantum Physics  2 