Why Is the Photon One-Point Function Zero in QED?

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SUMMARY

The photon one-point function in Quantum Electrodynamics (QED) is zero due to the requirement that the external photon must be attached to a QED vertex. According to Peskin's "An Introduction to Quantum Field Theory," neglecting the external photon propagator leads to an amplitude that does not contribute to the one-point function. Including the photon propagator results in the same diagram as replacing the current with the photon field, reinforcing the conclusion that the photon one-point correlation function is zero.

PREREQUISITES
  • Quantum Electrodynamics (QED) fundamentals
  • Understanding of Feynman diagrams
  • Knowledge of photon propagators
  • Familiarity with correlation functions in quantum field theory
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  • Study the derivation of the photon propagator in QED
  • Explore Feynman rules for QED interactions
  • Investigate the role of current density j_{\mu} in QED
  • Learn about correlation functions and their significance in quantum field theory
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Physicists, students of quantum field theory, and researchers focusing on Quantum Electrodynamics and its mathematical foundations.

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In 'an introduction to quantum field theory' by peskin, he writes: To analyze the photon one-point function, note that the external photon must be attached to a QED vertex. Neglecting the external photon propagator, this amplitude is therefore:

upload_2015-10-1_16-44-37.png


I really cannot justify this equation. Can anyone explain it to me?
 
Intuitively, the expression is essentially the diagram with the two fermion lines and vertex (by definition of j_{\mu}). Note the, "neglecting the external photon propagator." If you include the photon propagator as a factor, the expression gives rise to the same diagram as if the current were to be replaced by the photon field, i.e. the photon one-point correlation function.
 

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