Casimir energy for a piecewise uniform string

Journal Article · Thu Feb 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.1185· OSTI ID:6915915

Brevik, I ^[1]; Nielsen, H B ^[2]

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1. Division of Applied Mechanics, University of Trondheim-Norges Tekniske Hgskole, 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 closed string is calculated. The string consists of two parts I and II, endowed in general with different tensions and mass densities, although adjusted in such a way that the velocity of sound always equals the velocity of light. The dispersion equation is worked out under general conditions and the frequency spectrum is determined in special cases. When the ratio {ital L}{sub II}/L{sub I} between the string lengths is an integer, it is in principle possible to determine the frequency spectrum through solving algebraic equations of increasingly high degree. The Casimir energy relative to the uniform string is in general found to be negative, although in the special case {ital L}{sub I}=L{sub II} the energy is equal to zero. Delicate points in the regularization procedure are discussed; in particular, it turns out that a straightforward use of the Riemann {zeta}-function regularization method leads to an incorrect expression for the Casimir energy.

• OSTI ID: 6915915
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Journal Issue: 4 Vol. 41:4; ISSN 0556-2821; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CASIMIR EFFECT
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
MASS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES