Attractive or repulsive nature of Casimir force in D -dimensional Minkowski spacetime

Journal Article · Fri Feb 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.1300· OSTI ID:5845741

Caruso, F; Neto, N P ^[1]; Svaiter, B F ^[2]; Svaiter, N F ^[3]

---

1. Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290 Rio de Janeiro, Brazil (BR)
2. Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460 Rio de Janeiro, (Brazil)
3. Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290 Rio de Janeiro, (Brazil)

The dependence of Casimir energy (associated with a massless scalar field) on spacetime dimensionality ({ital D}) is shown to be strongly entangled with the type of geometric bounds and the kind of macroscopic boundary conditions imposed on the field. In the case of a massless scalar field satisfying Dirichlet boundary conditions in the presence of a hyperparallelepipedal cavity with {ital p} sides of finite length {ital L} and {ital D}{minus}{ital p}{minus}1 sides with length much greater than {ital L}, a new compact integral formula, more suitable to analyze the nature of the Casimir force, is obtained. The force is attractive if {ital p} is odd or for very large even values of {ital p}, irrespective of {ital D}. For each small even {ital p} there exists a critical spacetime dimension {ital D}{sub {ital c}}({ital p}) such that the force is repulsive if {ital D}{lt}{ital D}{sub {ital c}} and attractive otherwise. As a consequence, the instability of the semiclassical Abraham-Lorentz-Casimir model of the electron is proved to depend on the spacetime dimensionality.

• OSTI ID: 5845741
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
CASIMIR EFFECT
ELEMENTARY PARTICLES
ENERGY DENSITY
MASSLESS PARTICLES
MATHEMATICAL SPACE
MINKOWSKI SPACE
SCALAR FIELDS
SPACE
SPACE-TIME