Electric charge in quantum field theory

[paweld]

I have a question concerning the notion of electric charge in QFT.
What value of charge for electron should I use if I want to compute
the force acting on electron in some external electric field. Of course
in first approximation it is just elementary charge which value might
be found in
http://physics.nist.gov/cgi-bin/cuu/Value?e".

I wonder what value should I use if I wanted to compute the force
using some vertex corrections from QFT. I'm not asking if this is sensible.
I only want to understand the concept of charge in QFT. Let's assume
that the bare charge (the walue which appear in lagrangian) is
equal $$q_b$$, the electromagnetic potential renormalization
constant calculated in given order is equal $$Z_3$$ (this constant is chosen
so that in given order the photon propagator has at $$p^2=0$$
unit residue), elementary unit charge is $$e$$ and $$q$$
is the value of charge which I should use to compute force acting on electron
taking into account qft correction.

Is it true that $$q=\sqrt{Z_3} q_b=e$$?

 

[azntoon]

Yes, it is true that q = sqrt(Z_3) q_b = e. This is because the renormalization constant Z_3 is defined such that the photon propagator has a unit residue at p^2=0, and hence the effective charge of the electron is equal to the elementary charge e.