Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones

Abstract

Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion relations, theorems of counting, etc. As supports are measurable, their absolutely strict borders contradict the spirit of quantum theory and their quantum evolution leading to appearance of subtractions or certain needed flattening would be considered. "Flattening" of projectors introduce transitive zones that can be examined as a specification of adiabatic hypothesis or the Bogoliubov regulatory function in QED. For demonstration of their possibilities the phenomena of refraction and reflection of electromagnetic wave are considered; they show, in particular, the inevitable appearing of double electromagnetic layers on all surfaces that formerly were repeatedly postulated, etc. Quantum dynamics of projectors proves the neediness of subtractions that usually are artificially adding and express transient singularities and zones in squeezed forms. KEY WORDS:properties and projectors, quantum dynamics of projectors, flattening of projectors, transient zones, double layers, transient singularities IntroductionIn the classical monograph of von Neumann [ 1 ] had been stated that qualitative (alternative) properties of physical systems can be described by projective operators (projectors) indicating their complete presence or complete absence. To such primordial properties of all systems must be attributed the causality, locality, mass-spectrality. However, particular features of definite objects/ devices such as proportions of solid media, spatial or temporal restrictions of parameters magnitudes, passband of frequencies or limits of work duration of technical devices and so on also can be added with the expanding of such description of the (characteristic) properties of specific objects.