Schwinger-Dyson equations derivation

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SUMMARY

The discussion focuses on the derivation of Schwinger-Dyson equations, specifically addressing the confusion surrounding the appearance of the commutator in the final expression. Participants clarify that the delta functions emerge from Heaviside functions, and emphasize the importance of understanding the relationship between ##\theta(-t)## and ##\theta(t)##. The use of the chain rule for differentiation is highlighted as a critical step in resolving the confusion regarding the signs in the terms. Overall, the discussion provides clarity on the mathematical foundations necessary for deriving these equations.

PREREQUISITES
  • Understanding of Schwinger-Dyson equations
  • Familiarity with Heaviside and delta functions
  • Knowledge of commutators and anticommutators in quantum field theory
  • Proficiency in differentiation techniques, including the chain rule
NEXT STEPS
  • Study the derivation process of Schwinger-Dyson equations in detail
  • Learn about the properties and applications of Heaviside and delta functions
  • Explore the role of commutators and anticommutators in quantum mechanics
  • Review advanced differentiation techniques and their applications in physics
USEFUL FOR

This discussion is beneficial for theoretical physicists, graduate students in quantum field theory, and anyone interested in the mathematical foundations of particle physics.

simonjech
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This is the part of Schwinger-Dyson equations derivation. I did not understand how can we obtain the commutator in the last line of the picture. I understand why the delta functions appeared from Heaviside functions but there is no minus sign in any term so how can we get the commutator? Anticommutator would make more sence for me.
Screenshot_20230305_212957_Drive.jpg
 
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Write down ##\theta (-t)## in terms of ##\theta (t)##. Drawing the graph of ##\theta (-t)## helps.
 
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Or just use the chain rule for differentiation
 
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I think that i figured it out. The problem was that I did not realized that
Screenshot_20230306_154107_Math Editor.jpg
.
 
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