Fermionic Casimir effect with helix boundary condition

Abstract

In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Ref. \cite{Feng,Zhai3} is something like that between a Möbius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the ($D+1$)-dimensional space-time. For both massless and massive cases, there is a $Z_2$ symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity.

7 pages, 4 figures, published in Eur. Phys. J. C

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Cited by in corpus (10)

• Casimir Energy for a Coupled Fermion-Kink System and its stability
• Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• Quantum Spring
• Generalized Schlömilch's formulas and thermal Casimir effect of a fermionic rectangular box
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Generalized Quantum Spring
• Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension
• Topological Casimir effect in models with helical compact dimensions