Integration question in Peskin and Schroeder

In summary, the conversation discusses the last step of proving equation (2.51) in Peskin and Schroeder. The solution involves using the method of stationary phase, and a related post in a different thread provides further clarification. The exact solution (Bessel function) is also mentioned as playing a role in the limit.
  • #1
ianhoolihan
145
0
Hi all, I'm stuck with proving the last step of (2.51) in Peskin and Schroeder:
$$\begin{align} D(x-y) &= \frac{1}{4\pi^2}\int^\infty_m dE \sqrt{E^2 - m^2}e^{-iEt}\\
& \approx_{t \to \infty}\ \ e^{-imt}\end{align}$$

I've read on another post that the solution is to use the method of stationary phase, but I do not see how this applies, as [itex]E[/itex] is not a rapidly oscillating function...?

Thoughts appreciated,

Ianhoolihan
 
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  • #3
Thanks strangerep,

The thread I referred to was https://www.physicsforums.com/showthread.php?t=424778.

Your post does make it clearer, in that it stems from a limit of the exact solution (Bessel function). I will look through the details soon.

Cheers.
 

1. What is integration in Peskin and Schroeder?

Integration in Peskin and Schroeder refers to the mathematical process of finding the area under a curve or the sum of infinitesimal values. In the context of quantum field theory, integration is used to calculate physical quantities such as scattering amplitudes and correlation functions.

2. Why is integration important in Peskin and Schroeder?

Integration is important in Peskin and Schroeder because it allows us to calculate physical quantities that describe the interactions between particles. These calculations are crucial for understanding the behavior of quantum fields and predicting experimental results.

3. What techniques are used for integration in Peskin and Schroeder?

There are several techniques used for integration in Peskin and Schroeder, including the method of residues, Feynman parameterization, and dimensional regularization. These techniques help to simplify complex integrals and make them more manageable to solve.

4. How do I solve an integration question in Peskin and Schroeder?

To solve an integration question in Peskin and Schroeder, you will need to carefully follow the steps outlined in the textbook. This typically involves using one of the integration techniques mentioned above, setting up the integral correctly, and carefully evaluating each term in the integral.

5. What are some common pitfalls when doing integration in Peskin and Schroeder?

One common pitfall when doing integration in Peskin and Schroeder is making mistakes in setting up the integral. It is important to carefully read the question and make sure that you have the correct limits of integration and the correct functions to integrate. Another common pitfall is not paying attention to the convergence of the integral, which can lead to incorrect results.

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