Peskin book on QFT question -- 2 integrals for D(x−y)

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SUMMARY

The discussion focuses on solving two integrals for the function D(x-y) as presented in Peskin's book on Quantum Field Theory (QFT), specifically in Chapter 2, Section 2.4. The first integral relates to the asymptotic behavior as t approaches infinity, while the second integral requires transforming to polar-momentum coordinates and applying contour integration techniques. For further clarification, the Rolnick text, particularly Appendix D, provides additional insights into these methods.

PREREQUISITES
  • Familiarity with Quantum Field Theory concepts, particularly from Peskin's text.
  • Understanding of asymptotic analysis in mathematical physics.
  • Knowledge of contour integration techniques.
  • Experience with polar-coordinate transformations in integrals.
NEXT STEPS
  • Review Chapter 2 of Peskin's "An Introduction to Quantum Field Theory" for foundational concepts.
  • Study asymptotic behavior in mathematical physics to grasp the first integral's implications.
  • Learn about contour integration methods and their applications in complex analysis.
  • Examine Rolnick's Appendix D for detailed explanations on the polar-coordinate transformation.
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Students and researchers in theoretical physics, particularly those studying Quantum Field Theory and seeking to understand integral techniques in QFT applications.

Silviu
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Hello! Those who used Peskin's book on qft, in chapter 2, Causality (2.4) there are 2 integrals for ##D(x-y)##. Can someone explain to me how does he solve them, as I tried for a bit and didn't manage to do them (actually to get the behavior as ##t \to \infty##). Thank you!
 
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IF I've guessed correctly which integrals you mean...

For the 1st one (leading to asymptotic ##t\to\infty## behaviour), see my final post in this old thread.

For the 2nd, that's just a matter of passing to polar-momentum coordinates first, and then doing a contour integral. IIRC, there's a more detailed explanation in Rolnick, Appendix D. (If you want more detailed help, you'll probably need to start a thread in the HW forum and show your work.)
 

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