Weinberg 3.4 -- Derive the perturbation expansion....

[kushal3553]

Homework Statement

Basically I wanted to see if anyone would be willing to give me the solution to the 4th problem of the Weinberg textbook on quantum field theory. The exact question in the book is "Derive the perturbation expansion (3.5.8) directly from the expansion (3.5.3) of old-fashioned perturbation theory."

Homework Equations

The relevant equations include the Fourier representation of energy, the Dyson series for the s-matrix, etc.

The Attempt at a Solution

S[/B]o I'm new to physicsforums so I have no idea how to do physics equations on the computer using what I think is called latex. Also, my work spans quite a few pages but I don't think I've gotten anywhere that would be all that useful in solving the problem.Thank you in advance to those that are willing to help!

 

[Matterwave]

To type in latex, simply use the $ or # wrappers and write in the familiar latex codes. For example, you can quote my post to see how I wrote the below equation: $$S=\int_a^b \mathcal{L} dt$$

You will have to show some of your work, or at least tell us about your approach, before someone will help you here. :)

 

[kushal3553]

Ok, so basically I inserted the Fourier representation of the energy factors into eq. (3.5.3) and came up with a factor of $$e^(iE_a * t) * V_(by)*V_(ya) * e^(-iE_y * t)$$ within the two integrals and I thought maybe I could get V(t) somewhere through that and the rest of my work has to do with manipulating the expression in the integral to maybe get $$<phi_a|V(t)|phi_b>$$ by the end of the expression. I was unsuccessful in this endeavor and I noticed that in (3.5.8) many of the integrals run from negative infinity to t_n which I have no idea how that can be derived from the old-fashioned perturbation series.

 

[kushal3553]

bump

 

[kushal3553]

bump

 

[berkeman]

bump

You seriously have made no progress in the last 3 years on this?