Calculate Differential Cross Section, Amplitude from Lagrangian

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SUMMARY

The discussion focuses on calculating the differential cross section and amplitudes from a given Lagrangian in quantum mechanics. Participants emphasize the use of Feynman diagrams to derive the amplitude, followed by applying the standard formula for two-body scattering. The vertex factor is represented as iL, where field operators are substituted with plane wave forms. For further understanding, the book "Advanced Quantum Mechanics" by Sakurai is recommended as a key resource.

PREREQUISITES
  • Understanding of Feynman diagrams and their application in quantum field theory
  • Familiarity with the concept of differential cross sections in particle physics
  • Knowledge of Lagrangian mechanics and its role in quantum mechanics
  • Basic grasp of scattering theory and vertex factors
NEXT STEPS
  • Study the derivation of differential cross sections in quantum field theory
  • Learn how to construct and interpret Feynman diagrams for various interactions
  • Explore the application of the vertex factor in scattering processes
  • Read "Advanced Quantum Mechanics" by Sakurai for in-depth theoretical insights
USEFUL FOR

Physicists, graduate students in quantum mechanics, and researchers involved in particle physics who are looking to deepen their understanding of scattering processes and amplitude calculations.

johnahn
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Lagrangian I have is little bit massy so I don't write in here.

Like in ψψ(dagger) , or ψ∅ -> ψ∅, How can I calculate the differential cross section or total, or amplitudes?
 
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Use Feynman diagrams to calculate the amplitude and then use the standard formula for 2 body scattering?
 


to get vertex factor write iL,then replace field operators by plane wave forms.leave out all factors which are taken care by other things such as normalization factors etc.rest is vertex factor.You may find relevant things in book of sakurai 'advanced quantum mechanics'.
 

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