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

In summary: The second diagram, which Wikipedia calls "vacuumpolarization second order", 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.
  • #1
raracon
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TL;DR Summary
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?

VP.png
VPHO.png
 
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  • #2
Are you sure that the second diagram is a vacuum polarization diagram?
 
  • #3
Gaussian97 said:
Are you sure that the second diagram is a vacuum polarization diagram?
Yup
 
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  • #4
Well, it's not. It's light-by-light scattering.
 
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  • #5
Vanadium 50 said:
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
 
  • #6
I defer to your expertise as an 11th grader, then.
 
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  • #7
Vanadium 50 said:
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?
 
  • #8
raracon said:
Yeah, but on Wikipedia the second pic is described by the words: Vacuumpolarisation second order
Wikipedia has been known to be wrong. Just sayin’
 
  • #9
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.
 
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  • #10
vanhees71 said:
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.
 
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  • #11
Of course self-energy insertions to external legs have no observable consequences. That's the point of renormalization after all!
 

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

What is vacuum polarisation order?

Vacuum polarisation order refers to the phenomenon in which the electric field of a vacuum is modified by the presence of a strong external electric field. This results in the creation of virtual particles and an overall polarization of the vacuum state.

How does vacuum polarisation order affect particles?

Vacuum polarisation order affects particles by altering their properties, such as their mass and charge, due to the presence of virtual particles in the vacuum. This effect is known as vacuum polarisation or self-energy.

What is the significance of vacuum polarisation order?

Vacuum polarisation order plays a crucial role in quantum field theory and has implications for understanding the fundamental nature of particles and their interactions. It also has practical applications in areas such as quantum computing and high energy physics.

Can vacuum polarisation order be observed experimentally?

Yes, vacuum polarisation order has been observed experimentally through various methods, such as measuring the Lamb shift in atomic spectra or studying the Casimir effect. These experiments provide evidence for the existence of virtual particles and the effects of vacuum polarisation.

How is vacuum polarisation order related to quantum fluctuations?

Vacuum polarisation order is closely related to quantum fluctuations, as it is a manifestation of the uncertainty principle in quantum mechanics. The creation of virtual particles and the resulting polarization of the vacuum state are a result of the constant fluctuations of quantum fields at the microscopic level.

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