CASIMIR THEORY FOR THE PIECEWISE UNIFORM RELATIVISTIC STRING

The purpose of this paper is twofold: (1) A survey is given of recent developments in the Casimir theory for a piecewise uniform relativisti c string, relativistic meaning that the velocity of transverse waves i s always taken to be equal to c. The adaptability of this string model with respect to various regularization methods is pointed out. The mo st powerful regularization method for the present system is the contou r integration method. The Casimir energy turns out to be negative, and more so the larger is the number of pieces in the string. (2) Some ne w developments are presented: it is first shown how the requirement ab out continuity of the transverse force at the junctions can be derived from a variational principle. Thereafter the string is analysed when its junction points are endowed with electrical charges and placed in an external magnetic field. It the field is coplanar to the string, th en resonance effects in general occur for the excited transverse oscil lations. A closer study is made, using Green function methods of the t ransient motions ocurring if the field is time dependent. If the field , by contrast, is directed transversely to the string, then no influen ce occurs at all on the motion. (C) 1997 Academic Press.