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 relativistic string, relativistic meaning that the velocity of transverse waves is always taken to be equal to c. The adaptability of this string model with respect to various regularization methods is pointed out. The most powerful regularization method for the present system is the contour 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 new developments are presented: it is first shown how the requirement about 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, then resonance effects in general occur for the excited transverse oscillations. A closer study is made, using Green function methods of the transient motions ocurring if the field is time dependent. If the field, by contrast, is directed transversely to the string, then no influence occurs at all on the motion. (C) 1997 Academic Press.