Electromagnetic Casimir piston in higher-dimensional spacetimes

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.105020· OSTI ID:21502643

Teo, L P ^[1]

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1. Department of Applied Mathematics, Faculty of Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500, Semenyih, Selangor Darul Ehsan (Malaysia)

We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form MxN, where M is the four-dimensional Minkowski spacetime and N is an n-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in M is large. It is found that if the separation between the plates is much smaller than the size of N, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the (4+n)-dimensional Minkowski spacetime. However, if the size of N is much smaller than the separation between the plates, the leading term of the Casimir force is 1+h/2 times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where h is the first Betti number of N. In the limit the manifold N vanishes, one does not obtain the Casimir force in the four-dimensional Minkowski spacetime if h is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.

• OSTI ID: 21502643
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
CASIMIR EFFECT
CROSS SECTIONS
CYLINDERS
ELECTROMAGNETIC FIELDS
FOUR-DIMENSIONAL CALCULATIONS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PLATES
SPACE
SPACE-TIME