arXiv subjects

Volodimir Simulik

Publications and source records attributed to Volodimir Simulik.

4 recordsLinked to original sources

arXiv2026

The Birth of Quantum Mechanics and the Dirac Equation

The year 2025 marked the centennial of quantum mechanics, inaugurated by Heisenberg's matrix formulation and the foundational contributions of Pauli, Schrodinger, and Dirac. Concurrently, 2026 marks the centennial of the Klein - Gordon equation, the second-order relativistic wave equation from which both the Schrodinger and Dirac equations were derived. This article supplements the recent review published in J.Phys. A: Math.Theor.,58 (2025) 053001 by providing a more detailed examination of the formative period 1925 - 1928, with particular attention to contributions that have received insufficient recognition in the standard narrative. We reconstruct Kramers' independent derivation of the Dirac equation - obtained essentially simultaneously with Dirac's own result yet unpublished for seven years - and discuss its relation to Van der Waerden's group-theoretical approach. The role of Charles Galton Darwin in elucidating the physical content of the Dirac equation is also highlighted. In addition, we present two modern derivations not catalogued in the earlier review: one based on Operational Dynamical Modeling, which deduces the Dirac equation from relativistic Ehrenfest relations and the canonical commutation algebra, and one rooted in the Madelung hydrodynamic formulation. Three broad periods of quantum theory development -- foundational, consolidation, and the modern era of quantum information -- are briefly surveyed.

physics.hist-ph↗

arXiv2025

The Mass and Velocity of Light from Energy and Momentum Conservation

While the numerical value of the speed of light is known with extraordinary precision, its theoretical definition remains a subject of fundamental interest. We show that the definition of mass and velocity of light follow from the conserved quantities of the electromagnetic field. The proposed definition of the speed of light is always bounded from above by the phase velocity and equals it for plane waves. As a consequence, we obtain a generalization of Einstein's mass-energy relation for electromagnetic fields in media: $m = \varepsilon\mu E / c^2$. Hence, irrespective of the light's intensity, the electromagentic field in near-zero-index material is always massless. This approach offers new pedagogical insights into the fundamental nature of light propagation.

physics.optics↗

arXiv2019

On the hidden symmetries of relativistic hydrogen atom

The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above mentioned algebras commute with the operator of the Dirac equation in the external Coulomb field, and, therefore, determine the algebras of invariance of such Dirac equation. Hence, the spin s=(1,0) Bose symmetry of the Dirac equation for the free spinor field, proved recently in our papers, is extended here for the Dirac equation interacting with external Coulomb field. Relativistic hydrogen atom is modeling here by such Dirac equation. We are able to prove for the relativistic hydrogen atom both the fermionic and bosonic symmetries known from our papers about the case of non-interacting spinor field. New symmetry operators were found on the basis of new gamma matrix representations of the Clifford and SO(8) algebras, which were found recently in our papers. Hidden symmetries were found both in the canonical Foldy--Wouthuysen and in the covariant Dirac representations. The symmetry operators, which are simple and graceful in the Foldy--Wouthuysen representation, become non-local in the Dirac model.

math-ph↗

arXiv2014

Covariant local field theory equations following from the relativistic canonical quantum mechanics of arbitrary spin

The new relativistic equations of motion for the particles with spin s=1, s=3/2, s=2 and nonzero mass have been introduced. The description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. The manifestly covariant field equations that follow from the quantum mechanical equations, have been considered. The covariant local field theory equations for spin s=(1,1) particle-antiparticle doublet, spin s=(1,0,1,0) particle-antiparticle multiplet, spin s=(3/2,3/2) particle-antiparticle doublet, spin s=(2,2) particle-antiparticle doublet, spin s=(2,0,2,0) particle-antiparticle multiplet and spin s=(2,1,2,1) particle-antiparticle multiplet have been introduced. The Maxwell-like equations for the boson with spin s=1 and $m>0$ have been introduced as well.

quant-ph↗