The Casimir force on a piston in the spacetime with extra compactified dimensions.pdf

a r X i v : 0 8 0 1 .2 8 1 0 v 1 [ h e p - t h ] 1 8 J a n 2 0 0 8 The Casimir force on a piston in the spacetime with extra compactified dimensions Hongbo Cheng? Department of Physics, East China University of Science and Technology, Shanghai 200237, China Abstract A one-dimensional Casimir piston for massless scalar fields obeying Dirichlet bound- ary conditions in high-dimensional spacetimes within the frame of Kaluza-Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the prop- erties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model excluding one plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough. PACS number(s): 03.70.+k; 11.10Kk ?E-mail address: hbcheng@public4.sta.net.cn 1 In 1948 a remarkable macroscopic quantum effect describing the attractive force between two conducting and neutral parallel plates was predicted by Casimir [1]. The Casimir effect appears due to the disturbance of the vacuum of the electromagnetic field induced by the presence of boundary. Twenty years later Boyer researched on the Casimir effect for a conducting spherical shell to find that this kind of Casimir force is repulsive [2]. This effect is more complicated than we thought. Afterwards more efforts have been paid for the problem and related topics. All results brought attention to the