How to Calculate Gaussian Integrals with 4-Momentum in QFT?

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Homework Help Overview

The discussion revolves around calculating Gaussian integrals within the context of quantum field theory (QFT), specifically involving four-momentum. The original poster seeks assistance with five specific integrals related to their calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest starting with the last integral and consider differentiation under the integration sign for the others. There is a question regarding the definition of 'q' as four-momentum.

Discussion Status

Some guidance has been offered regarding potential approaches to the integrals, and references to external resources, such as a textbook, have been mentioned. Multiple interpretations of the problem and methods are being explored, but no consensus has been reached.

Contextual Notes

There is a mention of a specific textbook that may provide useful derivations, indicating that the original poster may be working within certain constraints or assumptions related to their study materials.

k54ledung
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I am doing some calculations in QFT. And, in my calculations, I have to deal with 5 Gaussian integrals as followed. Please help me calculate those 5 integrals. Thank you very much!
 

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you can start with the last one and some differentiation under integration signs would be useful for the first four.by the way that q is four momentum,right?
 
I don't know if you have access to Zee's QFT in a Nutshell textbook, but he has a helpful page ,or two, that shows how to derive those integrals near the beginning of the book.

You could probably find it on Amazon, as well, assuming it's one of the ones you can "look inside"
 
Thanks so much!:)
 

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