How Do You Derive the Klein-Gordon Propagator from Commutation Relations?

[HadronPhysics]

Homework Statement

I am reading Peskin's book on Chapter 2. I have a question about deriving the K-G propagator

Relevant Equations

$\bra 0|[\phi(x), \phi(y)] |0 \ket = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}} \left( e^{-ip(x-y)} - e^{ip(x-y)} \right) =\int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}}e^{-ip(x-y)} + \int \frac{d^3 p}{(2\pi)^3} \frac{1}{-2E_{p}}e^{-ip(x-y)}$

$r$

 

[malawi_glenn]

What is the question?

 

[Delta2]

Standard derivation of the K-G propagator ? ()

Sorry I got no clue which book he means and got no clue what is that propagator. I suspect it has something to do with QFT of which I know very little...

All I know is that K-G probably stands for Klein - Gordon and I don't even know why I am replying to this post, I vent sleep well but I just can't sleep and I feel I got something to do.

 

[malawi_glenn]

Standard derivation of the K-G propagator ?

Should be a more specific question, about some detail or something.

Relevant Equations:: $\bra 0|[\phi(x), \phi(y)] |0 \ket = \ldots$

Also it should read $\langle 0|[\phi(x), \phi(y)] |0 \rangle =$

Sorry I got no clue which book he means and got no clue what is that propagator. I suspect it has something to do with QFT of which I know very little...

Yeah it is QFT

 

[George Jones]

Homework Statement:: I am reading Peskin's book on Chapter 2.

No, you are reading the 1995 book by Peskin and Schroeder. The distinction is important because there is a 2019 book authored solely by Peskin.

Should be a more specific question, about some detail or something.

Yes, what is the specific difficulty? Something on pages 29 - 31?

 

[malawi_glenn]

The distinction is important because there is a 2019 book authored solely by Peskin.

But chapter 2 in that book "concepts of elementary particle physics" does not deal with scalar quantum field theory :)

 

[bob012345]

Homework Statement:: I am reading Peskin's book on Chapter 2. I have a question about deriving the K-G propagator
Relevant Equations:: $\bra 0|[\phi(x), \phi(y)] |0 \ket = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}} \left( e^{-ip(x-y)} - e^{ip(x-y)} \right) =\int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}}e^{-ip(x-y)} + \int \frac{d^3 p}{(2\pi)^3} \frac{1}{-2E_{p}}e^{-ip(x-y)}$

$r$

Welcome to PF!

Please elaborate what your specific question is and if it is an actual homework problem, please show your attempt at a solution first. Also, sometimes an answer can be found looking at relevant threads from the past which are pulled up at the bottom of this page. Thanks.

 

[berkeman]

Homework Statement:: I am reading Peskin's book on Chapter 2. I have a question about deriving the K-G propagator
Relevant Equations:: $\bra 0|[\phi(x), \phi(y)] |0 \ket = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}} \left( e^{-ip(x-y)} - e^{ip(x-y)} \right) =\int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_{p}}e^{-ip(x-y)} + \int \frac{d^3 p}{(2\pi)^3} \frac{1}{-2E_{p}}e^{-ip(x-y)}$

$r$

Thread has been closed as Substandard. The new OP has been asked to start a new thread with a better post, including details about what exactly is confusing them in this material. Thanks folks for trying.