How to calculate Feynman diagrams in phi^4

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SUMMARY

This discussion focuses on calculating Feynman diagrams in quartic scalar field theory, specifically referencing the lowest order diagrams from Srednicki's solutions. The calculation involves using vertices represented by the integral $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and recognizing that the first diagram includes two contractions $$\Delta (0)$$, leading to the expression $$\Delta (0)^{2} \int \frac{d^{4}x}{(2\pi)^{4}}$$. Participants recommend consulting resources such as Peskin and Schroeder, as well as Veltman's "Diagrammatica" for further insights.

PREREQUISITES
  • Understanding of Feynman diagrams and their components
  • Familiarity with quartic scalar field theory
  • Knowledge of integral calculus in four dimensions
  • Experience with quantum field theory textbooks, specifically Srednicki and Peskin & Schroeder
NEXT STEPS
  • Study the calculation methods outlined in "Diagrammatica" by Veltman
  • Explore the Feynman rules for quartic interactions in quantum field theory
  • Practice solving Feynman diagrams using Peskin and Schroeder as a guide
  • Investigate advanced topics in quantum field theory related to perturbation theory
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Students and researchers in theoretical physics, particularly those focusing on quantum field theory and Feynman diagram calculations.

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For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them.

What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the first diagram their would be two contractions $$\Delta (0)$$ because the propagators return to the place they originated at. So would the first diagram just be $$\Delta (0) ^{2} \int \frac{d^{4}x}{(2\pi)^{4}}$$

Self-studying is incredibly difficult! Any help would be much appreciated! :)
 

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Try finding your answer in this website:
http://bolvan.ph.utexas.edu/~vadim/classes/2004f.homeworks/HWpage.html

If it doesn't appear there then try searching for solutions to Peskin and Schroeder, try reading the book.

There's also the book called diagrammatica by Veltman if I am not wrong that should have a good description on how to calculate it for quartic term.
 

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