This survey is devoted to the history and the current state of the theory of regularized traces
of linear operators. The main focus is on operators with discrete spectrum. Several …

Теория следов линейных операторов начинается с фундаментального результата
линейной алгебры: матричный след линейного оператора инвариантен относительно …

Casimir energy is a nonlocal effect; its magnitude cannot be deduced from heat-kernel
expansions, even those including the integrated boundary terms. On the other hand, it is …

Green functions scattering method is generalized to consider mixing of electromagnetic
polarizations after reflection from the plane boundary between different media and applied …

The new exact formulas for the attractive Casimir force acting on each of the two identical
perfectly conducting plates moving freely inside an infinite perfectly conducting cylinder with …

We propose Green functions scattering method to obtain the Casimir–Polder potential
between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure …

The Casimir force is very weak, however it increases rapidly as the separation a decreases
and it becomes measurable when a∼ 1 µm or less. For plates 1cm in area with a= 0. 5 µm …

Abstract Theory of the Casimir effect is presented in several examples. Casimir–Polder-type
formulas, Lifshitz theory and theory of the Casimir effect for two gratings separated by a …

We discuss a systematic way to dimensionally regularize divergent sums arising in field
theories with an arbitrary number of physical compact dimensions or finite temperature. The …

We solve the diffraction problem for electromagnetic waves on a planar (2+ 1)-dimensional
layer with a given Chern–Simons action. The Casimir energy of a system of two parallel …