Why is there an additional prefactor in equation (12.52) of Peskin's QFT book?

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thatboi
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Hey all,
I am currently having trouble understanding equation (12.52) in Peskin's QFT book. Specifically the term for external leg corrections, in which they tack on an additional prefactor of ##(-ig)##. Normally with external leg prefactors, we don't see the coupling constant multiplied onto the field renormalization counterterm so why is such a prefactor included here?
Thanks.
 

FAQ: Why is there an additional prefactor in equation (12.52) of Peskin's QFT book?

Why is there an additional prefactor in equation (12.52) of Peskin's QFT book?

The additional prefactor in equation (12.52) arises from the normalization conventions used in quantum field theory. Specifically, it ensures that the calculated physical quantities, such as cross-sections and decay rates, are consistent with experimental results.

How does the prefactor affect the physical interpretation of the equation?

The prefactor affects the physical interpretation by scaling the amplitude of the process described by the equation. This scaling ensures that the theoretical predictions match the observed data. Without the correct prefactor, the computed probabilities of certain interactions would not align with empirical measurements.

Is the prefactor unique to equation (12.52) or does it appear in other equations as well?

The prefactor is not unique to equation (12.52); similar prefactors can appear in other equations throughout quantum field theory. These prefactors often arise from integrating out certain degrees of freedom or from specific normalization choices in the formulation of the theory.

Can the prefactor be derived from first principles?

Yes, the prefactor can be derived from first principles. It typically comes from the detailed calculation of Feynman diagrams and the application of the LSZ reduction formula, which connects the S-matrix elements with the Green's functions. The derivation involves careful consideration of the normalization of states and the factors associated with external lines in the diagrams.

Does the prefactor have any implications for renormalization or regularization procedures?

The prefactor can have implications for renormalization or regularization procedures, as it may affect the counterterms needed to cancel divergences in loop calculations. Properly accounting for these prefactors is crucial to ensure that the renormalized theory remains consistent and predictive. They help maintain the correct relationship between bare and renormalized quantities.

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