Greens function path integral representation

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SUMMARY

The forum discussion centers on the path integral representation of the Green's function as presented in the user's book. The user seeks clarification on transitioning from the standard trace formula for the Green's function, specifically equation 2.6, to the path integral form. They reference their lecture notes on many-body quantum field theory (QFT) as a potential resource for further understanding this complex topic.

PREREQUISITES
  • Understanding of Green's functions in quantum mechanics
  • Familiarity with path integral formulation
  • Knowledge of many-body quantum field theory (QFT)
  • Ability to interpret mathematical equations in physics
NEXT STEPS
  • Study the trace formula for Green's functions in quantum mechanics
  • Explore the path integral formulation of quantum mechanics
  • Review lecture notes on many-body QFT for deeper insights
  • Examine specific examples of Green's function applications in quantum field theory
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on quantum mechanics and quantum field theory, will benefit from this discussion.

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In my book the path integral representation of the green's function is given as that on the attached picture. But how do you go from the usual trace formula for the Green's function 2.6 to this equation?
 

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