(PS: this post was also posted at the quantum mechanics/field theory forum, but I did not get any replies there)(adsbygoogle = window.adsbygoogle || []).push({});

Often when one speaks about the effective QED coupling one defines it as

$$e = \frac{Z_2 Z_3^{1/2}}{Z_1} e_0 \ \ \ \ (*)$$

when ##Z_1 = Z_2## by the Ward identity this turns out to be ##Z_3^{1/2}e_0## and some authors just define the coupling to be this right away.

So why do some make a point that the effective coupling is really defined according to (*). In what sense is this the 'natural definition'?

I have thought about it, and the best answer I have come up with is the following:

For an effective coupling one wants a definition which captures as much information about the interaction as possible so that when one has a large effective coupling, one can also say that the probability for an interaction is large. This thus requires us to take in the effects from the propagator of the electron (Z_2), the propagator of the photon (Z_3) and the vertex function (Z_1). Since there are two electron propagators connected to each vertex one gets two factors of ##Z_2^{1/2}## while one gets just one factor of ##Z_3^{1/2}## from the photon propagator.

Any insights would be appreciated!

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# Definition of effective QED coupling.

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