Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-07-13
Phys.Lett.B691:167-172,2010
Physics
High Energy Physics
High Energy Physics - Theory
6 pages, 7 figures, published in PLB
Scientific paper
10.1016/j.physletb.2010.06.030
The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this paper, we choose a topology of the flat $(D+1)$-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio $r$ of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it \textit{quantum spring}. When $r$ is large, this force behaves like the Newton's law of universal gravitation in the leading order. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio $r$. Both forces are attractive and their behaviors are the same in two and three dimensions.
Feng Chao-Jun
Li Xin-zhou
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