Graduate Understanding the Use of Grassman Numbers in Fermionic Fields: A QFT Guide

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SUMMARY

This discussion focuses on the application of Grassmann numbers in the context of fermionic fields within Quantum Field Theory (QFT). The participant has a foundational understanding of quantum mechanics and classical fields, referencing texts such as Griffiths and Peskin & Schroeder. The inquiry specifically seeks clarity on the role of Grassmann numbers in the quantization process of fermionic fields, indicating a need for deeper comprehension of this mathematical tool.

PREREQUISITES
  • Familiarity with Quantum Mechanics, particularly operator theory and scattering matrices.
  • Understanding of Classical Field Theory as outlined in Goldstein's texts.
  • Knowledge of Quantum Field Theory principles from Peskin & Schroeder and Zee's "QFT in a Nutshell".
  • Basic comprehension of fermionic fields and their quantization processes.
NEXT STEPS
  • Study the mathematical foundations of Grassmann numbers and their properties.
  • Explore the role of Grassmann numbers in the path integral formulation of QFT.
  • Review specific examples of fermionic field quantization using Grassmann variables.
  • Investigate the implications of Grassmann numbers in the derivation of Feynman rules for fermions.
USEFUL FOR

This discussion is beneficial for graduate students in theoretical physics, researchers in quantum field theory, and anyone seeking to deepen their understanding of fermionic fields and the mathematical tools used in their quantization.

bengeof
My background is QM as done in Griffiths( So yes I have a background of operators, observables and scattering matrix), Classical fields as done in Goldstein and Particle physics as in Griffiths. Griffiths actually works out Feynman rules for QED and QCD. I've started QFT with Peskin and Schroeder and Zee's QFT in a nutshell. I need help in understanding the use of Grassman numbers in fermionic fields
 
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What is grassman numbers? I didn't understand the wiki article on it. . and how is it used in the quantization of fermionic fields ?

Thanks
 
bengeof said:
What is grassman numbers? I didn't understand the wiki article on it. . and how is it used in the quantization of fermionic fields ?

Thanks
This is far too general for us to be of much use without writing a textbook style introduction. You say you have read the Wiki page, exactly what about them did you run into problems with?
 
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Likes vanhees71 and PeterDonis

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