The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime

Abstract

The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper\cite{Feng}. In this paper, the Casimir effect of the quantum spring is investigated in $(D+1)$-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any $D$, which indicate a $Z_2$ symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the $\zeta$-function. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes.

9 pages, 5 figures, v2, massive case added, refs. added

References in corpus (6)

• Casimir forces between arbitrary compact objects
• Casimir force on a piston
• Casimir pistons with hybrid boundary conditions
• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• Quantum Spring from the Casimir Effect
• Casimir Pistons for Massive Scalar Fields

Cited by in corpus (9)

• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Fermionic Casimir effect with helix boundary condition
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Quantum Spring
• 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
• Topological Casimir effect in models with helical compact dimensions
• Generalized Quantum Spring
• Equivalence of zeta function technique and Abel-Plana formula in regularizing the Casimir energy of hyper-rectangular cavities