I What is the difference between first and second-order vacuum polarization?

[raracon]

TL;DR

What is the difference for i.e vaccumpolarisation of the lowest order and vacuumpolarisation second order?

What determines the order of the vacuumpolarisation? I've added 2 Feynman Diagrams for refference. The first one shows the vacuumpolarisation of the lowest order the second shows the vacuumpolarisation of the 2nd order. What is the difference?

 

[Gaussian97]

Are you sure that the second diagram is a vacuum polarization diagram?

 

[raracon]

Are you sure that the second diagram is a vacuum polarization diagram?

Yup

 

[Vanadium 50]

Well, it's not. It's light-by-light scattering.

 

[raracon]

Well, it's not. It's light-by-light scattering.

Yeah, but on Wikipedia the second pic is described by the words: Vacuumpolarisation second order

 

[Vanadium 50]

I defer to your expertise as an 11th grader, then.

 

[raracon]

I defer to your expertise as an 11th grader, then.

Nah, I am just madly confused haha. It is indeed Light by Light scattering, but why does it have that name given to it? Or how would a vacuumpolarisation second order look like?

 

[Nugatory]

Yeah, but on Wikipedia the second pic is described by the words: Vacuumpolarisation second order

Wikipedia has been known to be wrong. Just sayin’

 

[vanhees71]

What's called "vacuum polarization" is usually referring to the photon self-energy diagrams, i.e., Feynman diagrams with two external wiggly photon lines. So the one-loop 1st diagram is a vacuum-polarization diagram, the 2nd diagram has four external photon lines, and it describes the elastic scattering of photons. This is a process that's not included in classical electrodynamics, i.e., it is purely due to the radiative corrections of the quantized theory, QED. You can get a contribution to the vacuum polarization by connecting two of the external lines to an internal photon line. Another example is if you take the 1st one-loop diagram and draw a photon line connecting the two internal electron-positron lines. These are then two-loop contributions to the vacuum polarization of the photon.

 

[Vanadium 50]

he one-loop 1st diagram is a vacuum-polarization diagram

But a terrible example of one, as it has no measurable effects. Photon goes in, photon with the same kinematics comes out.

 

[vanhees71]

Of course self-energy insertions to external legs have no observable consequences. That's the point of renormalization after all!