We study the actions of the Lie algebra nsl(2,C) of SL(2,C) and the associated Casimir operator on the space of pseudodifferential operators of n variables. We describe the effect of the Casimir operator on a pseudodifferential operator in connection with the symbol map and construct an nsl(2,C)-invariant lifting of the symbol map.

From the SU(2) and SU(3) lattice QCD studies of the static potential between color charges in various dimensional representations, there arises the Casimir scaling hypothesis for the intermediate distance force [ 1, 2, 3]. This hypothesis tells that the ratio of forces associated with various dimensional representations of color charges, for a given color group, is determined by that of eigenva...

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects’ scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the intern...

We study interactions between localized scatterers on metallic carbon nanotubes by a mapping onto a onedimensional Casimir problem. Backscattering of electrons between localized scattering potentials mediates long-range forces between them. We model spatially localized scatterers by local and nonlocal potentials and treat simultaneously the effects of intravalley and intervalley backscattering....

In this paper the Casimir effect for parallel plates at finite temperature in the presence of compactified universal extra dimensions is analyzed. We show the thermal corrections to the effect in detail. We investigate the Casimir effect for different size of universal extra dimensions. PACS number(s): 11.10.Kk, 04.62.+v ∗E-mail address: [email protected]

Multiple scattering formulations have been recently rediscovered as a method of studying the quantum vacuum or Casimir interactions between distinct bodies. The methods are hardly new, but increased computing power and advances in understanding allow us to extract information efficiently. Here we review the method in the simple context of δ-function potentials, so-called semitransparent bodies....

The Casimir effect for a three-parallel-plate system at finite temperature within the frame of five-dimensional Randall-Sundrum models is studied. In the case of RandallSundrum model involving two branes we find that the Casimir force depends on the plates distance and temperature after one outer plate has been moved to the distant place. Further we discover that the sign of the reduced force i...

In 1948 Casimir predicted an unexpected quantum field theory (QFT) effect: as a consequence of distorting the vacuum of the quantized electromagnetic field, two conducting and neutral parallel plates should attract each other with a force proportional to the inverse of the fourth power of their separation [1] (for general reviews on the Casimir effect, see Refs. [2]; for an introductory guide, ...