Casimir force in brane worlds: Coinciding results from Green's and zeta function approaches

Journal Article · Tue Jun 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.126013· OSTI ID:21408129

Linares, Roman; Morales-Tecotl, Hugo A ^[1]; Pedraza, Omar ^[2]

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1. Departamento de Fisica, Universidad Autonoma Metropolitana Iztapalapa, San Rafael Atlixco 186, Codigo Postal 09340, Mexico Distrito Federal (Mexico)
2. Centro de Estudios en Fisica y Matematicas Basicas y Aplicadas, Universidad Autonoma de Chiapas, 4a. Oriente Norte 1428, Tuxtla Gutierrez, Chiapas (Mexico)

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 that 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 hypervolume 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 hypervolume 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.

• OSTI ID: 21408129
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BRANES
CASIMIR EFFECT
EIGENFUNCTIONS
FLUCTUATIONS
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GREEN FUNCTION
PLATES
SPACE-TIME
VARIATIONS