Generating function of n-point function

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SUMMARY

The discussion centers on the feasibility of constructing a generating function Z[J] with a quadratic or cubic dependence on the source J(t), specifically in the form Z[J]=∫Dq exp{S[q] + ∫ J²(t) q(t)dt}. It concludes that introducing a J² term complicates the calculation of n-point functions, as setting J=0 would eliminate all q-dependent terms, rendering the approach unreasonable for generating n-point functions. The participants emphasize the necessity of linear dependence on J for valid n-point function calculations.

PREREQUISITES
  • Understanding of generating functions in quantum field theory
  • Familiarity with n-point functions and their significance
  • Knowledge of functional integrals and path integrals
  • Basic concepts of source terms in field theory
NEXT STEPS
  • Research the role of linear dependence in generating functions
  • Explore the implications of quadratic and cubic terms in quantum field theory
  • Study the calculation methods for n-point functions in various contexts
  • Investigate the effects of source term modifications on functional integrals
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory, as well as graduate students seeking to deepen their understanding of generating functions and n-point function calculations.

guilhermef
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Hey guys, I have a doubt.

I was wondering if it is possible to have a generating function Z[J] where its integral has not a linear dependence on J(t), but a quadratic or even cubic dependence, like Z[J]=∫Dq exp{S[q] + ∫ J²(t) q(t)dt}, and how this would alter the calculation of the n-point functions.

Thaks!
 
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It's not reasonable b/c you introduce the source J only to construct the n-point functions for vanishing source J=0; with a J² term after setting J=0 all q-depenedent terms would vanish
 

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