We calculate the Casimir energies due to matters with various boundary conditions along two compact directions in six-dimensional T 2 compactification. We discuss whether the Casimir forces are attractive or repulsive forces. On the theories with extra dimensions, the Casimir energy plays a crucial role in the mechanism for stabilizing the size of extra dimensions. Finally we argue a procedure ...

We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L×b rectangular box, divided by a movable partition (piston) into two boxes of dimensions a × b and (L − a) × b. We compute the Casimir force on the piston in the limit L → ∞. Regardless the value of a/b, the piston is attracted to the nearest end of the box. Asymptotic expressions for th...

Casimir effect is the attractive force which acts between two plane parallel, closely spaced, uncharged, metallic plates in vacuum. This phenomenon was predicted theoretically in 1948 and reliably investigated experimentally only in recent years. In fact, the Casimir force is similar to the familiar van der Waals force in the case of relatively large separations when the relativistic effects co...

We compute the influence of an external magnetic field on the Casimir energy of a massive charged scalar field confined between two parallel infinite plates. For this case the obtained result shows that the magnetic field inhibits the Casimir effect. The Casimir effect can be generally defined as the effect of a non-trivial space topology on the vacuum fluctuations of relativistic quantum field...

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC’s and Casimir experiments involving structures that approx...

Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nanoand microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonst...

The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to ...

We consider a Casimir cavity, one plate of which is a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the far infrared) of the reflection coefficient of the film engenders a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very sma...

Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for ‘small’ Lie algebras and suitable for treatment by computer algebra. A very large body of new results emerges in the forms, a) of id...