Casimir effect in four simple situations - including a noncommutative two-sphere

Casimir effect of a topologically nontrivial two-dimensional space-time, through Krein space quantization [1,2], has been calculated. In other words, auxiliary negative norm states have been utilized here. Presence of negative norm states play the role of an automatic renormalization device for the theory. The negative norm states (which do not interact with the physical world) could be chosen in two perspective. In the first case our method results in zero or vanishing value...

We present new results for Casimir forces between rigid bodies which impose Dirichlet boundary conditions on a fluctuating scalar field. As a universal computational tool, we employ worldline numerics which builds on a combination of the string-inspired worldline approach with Monte-Carlo techniques. Worldline numerics is not only particularly powerful for inhomogeneous background configurations such as involved Casimir geometries, it also provides for an intuitive picture of...

Casimir interactions (due to the massless scalar field fluctuations) of two surfaces which are close to each other are studied. After a brief general presentation, explicit calculations for co-axial cylinders, co-centric spheres and co-axial cones are performed.

We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by the term $\lambda (u \cdot \partial \phi) ^{2}$, where the parameter $\lambda$ and the background vector $u^{\mu}$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D$, the Casimir stress by using Green's function techniques for two specific choices of the vector ...

We present the foundations of a new approach to the Casimir effect based on classical ray optics. We show that a very useful approximation to the Casimir force between arbitrarily shaped smooth conductors can be obtained from knowledge of the paths of light rays that originate at points between these bodies and close on themselves. Although an approximation, the optical method is exact for flat bodies, and is surprisingly accurate and versatile. In this paper we present a sel...

We compute the Casimir energy for a free scalar field on the spaces $\,R^{m+1}\,\times\,\tilde S^2\,$ where $,\tilde S^2\,$ is two-dimensional deformed two-sphere.

Starting from the construction of the free quantum scalar field of mass $m\geq 0$ we give mathematically precise and rigorous versions of three different approaches to computing the Casimir forces between compact obstacles. We then prove that they are equivalent.

Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of geometries. For the planar case a finite universal force is automatically found. For curved geometries formally divergent expressions are encountered which we argue are...

Two fundamental signatures of Quantum Mechanics are tunnelling and the Casimir effect. We examine the ground state energetic properties of a scalar field confined on a $D$-dimensional sphere, and subjected to these two effects. We focus on $D=2$ and $D=3$, with a non-minimal coupling of a massless scalar field to curvature, which provides a radius-dependent effective mass. This scenario allows tunnelling to be more important than the Casimir effect, in a certain regime of par...

We consider the Casimir interaction between two spheres in $(D+1)$-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coord...