QED vacuum polarization – a new analysis

On October 22, 2025 we left the analysis of the QED vertex correction incomplete. In our previous blog post we (maybe) were able to complete the analysis.

Let us next attack QED vacuum polarization, based on the insights we got from the vertex correction. On November 4, 2025 we wrote a previous detailed analysis of vacuum polarization.

Is the Feynman rule that a closed fermion loop adds -1 correct?

In this blog we have criticized that rule. Let us have the following Feynman diagram:

 

                                         ___

                               e-   /         \

   photon      ~~~~~                 ~~~~~

                               e+  \_____/

The diagram, with the -1 rule claims that the phase of the photon changes 180 degrees, even though it does not interact with any outside object. That cannot happen with classical waves. We do not believe it is possible with quantum waves, either.

https://www.bohrium.com/en/sciencepedia/feynman/keyword/fermion_loops

The text in the link says that a fermion loop involves an odd number of fermion field swaps, and that the factor -1 comes from the fact that fermion fields anticommute.

https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem

***  WORK IN PROGRESS  ***