Casimir theory for the piecewise uniform relativistic string

Journal Article · Sun Jun 01 04:00:00 EDT 1997 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1997.5679· OSTI ID:538359

Berntsen, M H; Brevik, I ^[1]; Odintsov, S D ^[2]

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1. Department of Applied Mechanics, Norwegian University of Science and Technology, N-7034 Trondheim (Norway)
2. Departimento de Fisica, Universidad del Valle, A.A. 25360 Cali (Colombia)

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 analyzed when its junction points are endowed with electrical charges and placed in an external magnetic field. If the field is {ital 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 occurring if the field is time dependent. If the field, by contrast, is directed {ital transversely} to the string, then no influence occurs at all on the motion. {copyright} 1997 Academic Press, Inc.

• OSTI ID: 538359
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 257; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACTION INTEGRAL
ANALYTIC FUNCTIONS
CASIMIR EFFECT
GREEN FUNCTION
LORENTZ FORCE
RELATIVISTIC RANGE
RENORMALIZATION
STRING MODELS
VARIATIONAL METHODS