The Study On Casimir Effect Of Two New Models

On the basis of a brief review of Casimir effect, this thesis focuses on the Casimir effect between two parallel conducting plates in the presence of compactified universal extra dimensions. The radius of the universal extra dimensions is decided by comparison with the experiment. Another study of the thesis is the Casimir effect of the piston model. The effect of the mass of scalar field and geometric factor, namely the ratio of box sides on the Casimir force on the piston is discussed, which is compared with the work of the others. The thesis includes the following sections:Firstly, a simple review of the proposal of Casimir effect, the development of Casimir effect in the theory and experiment, and the role of Casimir effect in physics and new technology is given. Secondly, we make a brief introduction to zeta function, which is an important technique in dealing with Casimir effect. The third section focuses on the Casimir effect between two parallel conducting plates within the framework of Kaluza-Klein theory in the presence of compactified universal extra dimensions. Assuming that the extra dimensions possess the same radius asR , we derive Casimir energy density and Casimir force density through Epstein zeta function regularization technique. The range of the radius R of the universal extra dimensions can be restricted by comparison with experimental data. In the fourth section, we make a research for the Casimir effect of the piston in the massive scalar field. The last section is the summary of the thesis.The main conclusion of this thesis and its significance is that the radius of extra dimensions is decided through the study of Casimir effect, which is different from the previous study of the extra dimensions problem. Piston model is a new model in the research of Casimir effect, which has considerable applicable potential in nanotechnology.