Piecewise Uniform String Of The Casimir Energy

Fifty years ago Casimir calculated the energy between two large uncharged conducting plales and found that the force on the plates was attractive. It was later called the Casimir effect. The energy was so called the Casimir energy. The Casimir energy can be considered as the polarization of the vacuum energy of quantized fields due to the distortion caused by the presence of boundaries, curvature of the space-time manifold or some background fields.The effect caused by other boundaries such as spherical and rectangular boundaries was also discussed. The Casimir energy of extended objects, such as strings and membranes has been investigated since 80's. The Casimir energy for membranes was discussed by Kikkawa and Yamasaki, Shi and Li independently. Brevik and Nielsen calculated the Casimir energy for the transverse oscillations of a piecewise closed bosonic string. The Casimir energy for a string at finite temperature has also been discussed by them. Lu and Huang extended their discussion to fermionic strings and Green-Schwarz superstrings. In this paper, the Casimir energy for various string loop systems, such as closed bosonic strings, multiloop strings and connected string loops is calculated. We compare the results of different systems and discuss some related topics.This paper was arranged as follows. In Chapter One, we discussed the concept of Casimir energy and calculated the Casimir energy between two large uncharged conducting plates. The role of the Casimir effect in different fields of physics was emphasized. The accomplishment during the last years including the experiments of the Casimir energy was discussed.In Chapter Two, as a simple example, we discussed the Casimir energy for piecewise bosonic strings composed by two segments. Some regularization. such as cut-off method, contour integration method and general ?-function method, used in calculating Casimir energy was discussed too.In Chapter Three, we continuously discussed the Casimir energy for some more complicated piecewise uniform strings. Firstly the Casimir energy for both open and closed piecewise uniform bosonic string systems with either untwised or twistedcontinuous conditions at junction points was discussed. Then the Casimir energy for closed piecewise uniform bosonic string systems composed by 2N segments was investigated.In Chapter Four, the Casimir energy for various string loop systems, such as closed bosonic strings, multiloop strings and connected string loops was calculated. We compared the results obtained from different systems. According to the high or low of the energy, we can decide what system is more stable. Furthermore we can also know the direction in string loop system evolution.There are a brief summery and some discussion in the end of this paper.