What is the functional iW[J] for a system with 2 sources or 3 sources?

[Hymne]

Hello!

I have a hard time getting to know what this exponential W(J) really is about. What is it even called?

Zee writes:

Z(J) = Z(J=0) * e^(i W(J)), and I suppose that this is the term that should be evaluated by summing over all possible pair of sources?

What is W(J) for a system with 2 sources or 3 sources?

Thanks really much!

 

[Hymne]

Hmm, I just wrote in my notes:

"The interpretation of W(J) is that we sum the amplitudes for all possible interactions between our sources."

Could somebody with more insight maybe just give me a right or wrong here?

 

[dextercioby]

W(J) is called the generating functional for the unconnected Green functions. The approach to QFT based on path integrals is well explained in the QFT books written by P. Ramond, D. Bailin and A. Love, L.H. Ryder. It all can be traced back to the 1965 book by Feynman and Hibbs.

 

[naima]

You can find this on the https://www.physicsforums.com/showthread.php?t=422296"
LAHLH recommended Srednicki's Textbook. You can download it on Srednicki Site

 

[RedX]

Hello!

I have a hard time getting to know what this exponential W(J) really is about. What is it even called?

Thanks really much!

iW[J], when multiplied by -kT, is a functional that's equal to the difference in Helmholtz free energy of the vacuum and one with sources J (at least when using real values of time).