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

TL;DR

This paper explores the properties of physical systems related to response function supports, revealing how transitive zones and transient singularities influence phenomena like refraction and reflection, with implications for quantum theory and electromagnetic surface layers.

Contribution

It introduces the concept of flattening projectors and transitive zones, linking them to adiabatic hypotheses and regulatory functions in QED, providing new insights into surface phenomena and quantum dynamics.

Findings

Double electromagnetic layers on surfaces are inevitable.

Flattening of projectors reveals transient singularities.

Quantum evolution involves subtractions and 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.