English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quantum field theory (QFT) is supposed to be gauge invariant. However it hasbeen well established that a direct calculation of the vacuum polarizationtensor produces a non-gauge invariant result. In this paper it will be shownthat this problem is due to the fact that there is a lower bound to the freefield energy in QFT. The vacuum polarization tensor will be calculated in 1+1dimensional space-time and is shown not to be gauge invariant. The gaugeinvariance of the theory can be restored through a regularization procedurewhich eliminates the non-gauge invariant terms. However it will be shown thatthis will impact the free field energy. If the free field energy is defined sothat the vacuum state has an energy of zero then the impact of regularizationis to introduce states whose free field energy is less than zero.

The Vacuum Polarization tensor in 1+1 dimensional space-time