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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Casimir force encodes the structure of the field modes as vacuum fluctuationsand so it is sensitive to the extra dimensions of brane worlds. Now, in flatspacetimes of arbitrary dimension the two standard approaches to the Casimirforce, Green's function and zeta function, yield the same result, but for braneworld models this was only assumed. In this work we show both approaches yieldthe same Casimir force in the case of Universal Extra Dimensions andRandall-Sundrum scenarios with one and two branes added by p compactdimensions. Essentially, the details of the mode eigenfunctions that enter theCasimir force in the Green's function approach get removed due to theirorthogonality relations with a measure involving the right hyper-volume of theplates and this leaves just the contribution coming from the Zeta functionapproach. The present analysis corrects previous results showing a differencebetween the two approaches for the single brane Randall-Sundrum; this was dueto an erroneous hyper-volume of the plates introduced by the authors when usingthe Green's function. For all the models we discuss here, the resulting Casimirforce can be neatly expressed in terms of two four dimensional Casimir forcecontributions: one for the massless mode and the other for a tower of massivemodes associated with the extra dimensions.

Casimir force in brane worlds: coinciding results from Green's and Zeta function approaches