Casimir theory for the piecewise uniform string: Division into 2[ital N] pieces

Journal Article · Wed Feb 15 04:00:00 EST 1995 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.51.1869· OSTI ID:6580904

Brevik, I ^[1]; Nielsen, H B ^[2]

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1. Applied Mechanics, The Norwegian Institute of Technology, N-7034 Trondheim (Norway)
2. The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)

The Casimir energy for the transverse oscillations of a piecewise uniform string in Minkowski space is calculated. The string consists in general of 2[ital N] pieces of equal length, of alternating type I and type II material, endowed with different tensions [ital T][sub I], [ital T][sub II] and mass densities [rho][sub I], [rho][sub II] but adjusted in such a way that the velocity of sound always equals the velocity of light. This string model (with [ital N]=1) was introduced by the present authors in 1990. In the present paper, the governing equations are formulated in the case of arbitrary integers [ital N], although detailed calculations are restricted to the case [ital N]=2, i.e., a four-piece string. The Casimir energy is regularized using (i) the contour integration technique introduced by van Kampen, Nijboer, and Schram, and (ii) the Hurwitz [zeta]-function technique introduced by Li, Shi, and Zhang. The energy is found as a function of the tension ratio [ital x]=[ital T][sub I]/[ital T][sub II]. The finite temperature version of the theory is also given.

• OSTI ID: 6580904
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 51:4; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CASIMIR EFFECT
COMPOSITE MODELS
ENERGY
EXTENDED PARTICLE MODEL
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MINKOWSKI SPACE
OSCILLATIONS
PARTICLE MODELS
QUARK MODEL
SPACE
STRING MODELS