Bare Charges of Identical Particles: Is It Possible?

[Riposte]

For two particles which have identical physical charges (say under electromagnetism), are the bare charges necessarily the same? Since the physical charge is related to the bare charge by photon and particle renormalization factors, I don't see how this could be the case in general.

In some sense, the bare charges are fundamental and therefore having two distinct charges renormalize to be identical strikes me as fine-tuned. Any thoughts?

 

[TriTertButoxy]

This fine-tuning is avoided thanks to gauge-invariance. A consequence of gauge-invariance is the Ward identity, which tells us that the charges will renormalize in the same way so as to preserve equality.

 

[Riposte]

Thanks, I think I get it now. In the terminology of Peskin/Schroeder we have:

eZ1 = e0 Z2 Z3^(1/2),
e'Z1' = e0 Z2' Z3^(1/2),

for two particles with the same bare charge. The Ward identity forces Z1 = Z2 and Z1' = Z2', and therefore the two must have the same physical charge as well