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

Abstract

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

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Cited by in corpus (5)

• On localization of universal scalar fields in a tachyonic de Sitter thick braneworld
• A de Sitter tachyonic braneworld revisited
• Casimir Energy for a Coupled Fermion-Kink System and its stability
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Equivalence of zeta function technique and Abel-Plana formula in regularizing the Casimir energy of hyper-rectangular cavities