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Source-Free Electromagnetism's Canonical Fields Reveal the Free-photon Schrödinger Equation (by Steven K. Kauffmann): Abstract: Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The source-free version of Maxwell's equations is purely dynamical, first-order in time and has well-defined nonnegative conserved field energy but is decidedly noncanonical. That should long ago have made source-free Maxwell equation canonical Hamiltonization a research priority, and afterward, standard textbook fare, but textbooks seem unaware of the issue. The opposite parities of the electric and magnetic fields and consequent curl operations that typify Maxwell's equations are especially at odds with their being canonical fields. Transformation of the magnetic field into the transverse part of the vector potential helps but is not sufficient; further simple nonnegative symmetric integral transforms, which commute with all differential operators, are needed for both fields; such transforms also supplant the curls in the equations of motion. The canonical replacements of the source-free electromagnetic fields remain transverse-vector fields, but are more diffuse than their predecessors, albeit less diffuse than the transverse vector potential. Combined as the real and imaginary parts of a complex field, the canonical fields prove to be the transverse-vector wave function of a time-dependent Schrodinger equation whose Hamiltonian operator is the quantization of the free photon's square-root relativistic energy. Thus proper quantization of the source-free Maxwell equations is identical to second quantization of free photons that have normal square-root energy. There is no physical reason why first and second quantization of any relativistic free particle ought not to proceed in precise parallel, utilizing the square-root Hamiltonian operator. This natural procedure leaves no role for the completely artificial Klein-Gordon and Dirac equations, as accords with their grossly unphysical properties. http://prespacetime.com/index.php/pst/article/view/141

Analysis of the Problem of Relation between Geometry and Natural Sciences (by Temur Kalanov): Abstract: The work is devoted to analysis of an actual problem – the problem of relation between geometry and natural sciences. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown within the framework of this basis that geometry represents field of natural sciences. Definitions of the basic concepts "point", "line", "straight line", "surface", "plane surface", and “triangle” of the elementary (Euclidean) geometry are formulated. The natural-scientific proof of the parallel axiom (Euclid’s fifth postulate), classification of triangles on the basis of a qualitative (essential) sign, and also material interpretation of Euclid’s, Lobachevski’s, and Riemann’s geometries are proposed. http://prespacetime.com/index.php/pst/article/view/143