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| viXra.org > Mathematical Physics > 2609 |
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[5] viXra:2609.0073 [pdf] submitted on 2026-09-25 19:05:32
Authors: Mat Hunt
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Claims of "scalar", "longitudinal" or "Tesla" electromagnetic waves often combine threedistinct phenomena: longitudinal electric-field components in anisotropic media, superluminalphase or group velocities, and an additional propagating scalar degree of freedom. Weseparate these questions and derive the relevant results from first principles. First, source-free Maxwell electrodynamics with tensor permittivity and permeability is reduced to itsplane-wave eigenvalue problem. The Gauss constraint is shown to make the displacementfield, rather than the electric field, transverse to the wave vector; an explicit anisotropicexample consequently has a predominantly longitudinal electric field and a phase velocityexceeding the vacuum light speed. The Poynting theorem is then derived for a dispersiveanisotropic medium, leading to the Brillouin energy density and energy velocity and showingwhy a superluminal phase velocity does not imply superluminal energy or signal propagation.Second, a genuine scalar degree of freedom is introduced through a Lorentz- and gauge-invariant dilaton-like action. All Euler—Lagrange equations are derived explicitly. Gauge,translation and Lorentz symmetries are treated with Noether’s theorem, yielding charge,energy—momentum and angular-momentum/boost conservation laws. Linearisation about astatic electric background gives the full mixed scalar—electromagnetic dispersion relation, itsnearly massless distinguished limit, and a scalar-associated branch which is purely longitudinalelectrically and has zero magnetic perturbation for propagation parallel to the backgroundfield. The same action gives a finite-electrode voltage-dependent capacitance; this predictionis derived using the Green function of the scalar equation. Existing scalar—photon andresonator searches already constrain the coupling strongly, making large effects in the minimalunscreened theory implausible. We finally formulate direct static and dynamical experimentaltests of the remaining longitudinal mode.
Category: Mathematical Physics
[4] viXra:2609.0064 [pdf] submitted on 2026-09-23 10:19:08
Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.
In this paper, we develop an observation into a precise operator-theoretic program. For a zero written as ρ=σ+it, the imaginary part of the energy is t(1-2σ). Hence, for every non-real zero in the critical strip, E_ρis real precisely on the critical line. The result shows the Riemann hypothesis is the assertion that all quadratic zeta energies are real. This paper then formulates the Hamiltonian structure required to turn this equivalence into a proof. The proposed operator is not a finite spectral fit, instead, it is a modular-arithmetic Hamiltonian built on logarithmic space, prime translations, an arithmetic boundary domain, a prime-power trace formula and determinant closure with the completed zeta function. The main theorem is conditional since if such a self-adjoint operator has determinant ξ(s) in the spectral coordinate s(1-s), then all non-trivial zeros lie on critical line.
Category: Mathematical Physics
[3] viXra:2609.0044 [pdf] submitted on 2026-09-16 20:49:48
Authors: Enrico Stretti
Comments: 20 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
This work introduces a discrete geometric model for the construction of a circle, basedon the hypothesis of a quantized space and the strict exclusion of the analytical continuum. The circular domain does not emerge as the limit of regular polygons, but rather from the progressive development of elementary circular sectors of increasing angular width associated with a step-by-step elongation of discrete radius; these sectors extend from the vertical axis of the circle, structuring their evolution into a numerical staircase pattern. A rectification procedure for the profile of thisstaircase is defined by means of a cutting line passing through the midpoints of the individual steps, thereby isolating right-trapezoid-shaped sections equivalent to the circular sectors of the discrete circle. The ordered accumulation of these elements reduces the measurement of the enclosed area to that of a corresponding equivalent isosceles right triangle. Under specific conditions of structural proportionality—and using a geometric equivalence constant (γ = 5/2) derived from the intrinsic properties of the configuration—it is demonstrated that the construction of this specific discrete model is governed by the exact dimensionless constant k = 25/8, which operates independently of the traditional analytical value of π.
Category: Mathematical Physics
[2] viXra:2609.0038 [pdf] submitted on 2026-09-13 09:59:31
Authors: Volodymyr Krasnoholovets
Comments: 22 Pages.
Real physical space, as a purely mathematical structure built according tothe rules of set theory, topology, and fractal geometry, was proposed by MichelBounias (1943-2003) and the author. It emerges as a mathematical lattice ofprimary topological balls, which was named a tessellattice, and the size of acell/ball in the tessellattice is comparative with the Planck length, ∼ 10^{−35} m.Discrete fractal properties of the lattice allow the prediction of scales at whichsubmicroscopic to cosmic structures should occur. This approach allows thedevelopment of a submicroscopic concept of physics, which describes Natureat a much deeper level than offered by the quantum-mechanical formalismdeveloped at the atom scale, ∼ 10^{−10} m. In addition, the approach makesit possible to define such fundamental physical notions as mass and chargefrom first submicroscopic principles, and this actually means that fundamentalmathematics lays down the basic concepts of physics.
Category: Mathematical Physics
[1] viXra:2609.0033 [pdf] submitted on 2026-09-12 00:50:54
Authors: Richard D. Lockyer
Comments: 32 pages plus 8 appendices
Attempts to apply Octonion Algebra to the Standard Model have involved creating a matrix algebra representing Octonion Algebra operating on itself, an adjacent algebra. Each used only one of sixteen Octonion division algebra orientations, and favored left application. This manuscript first demonstrates how proper use of Octonion Algebra for mathematical physics must give consideration to all sixteen in an algebraic orientation covariant fashion if one is to avoid pathological outcomes when the same analysis is repeated using another orientation.Properly constructed 8x8 adjacent algebra matrices generate an algebraic orientation covariant left/right application inclusive group also closed for all Octonion algebraic orientation changes. Orientation closed pairs of conjugacy classes lead to sixteen class equivalence partitions. Eight bracket/orientation closed Lie algebras are created from them, which demonstrate the orientation of each 8x8 adjacent algebra matrix position is fixed. Seven Lie algebras have four ideals in 4x4 submatrices that pair up to occupied rows/columns directly related to the seven Quaternion subalgebra indexes or their basic quad index set. From these, fourteen unique skew-Hermitian Dirac gamma matrix bases for su(4) are created, and within each six skew-Hermitian Pauli matrix su(2) bases. 28 unique su(2) bases span the 8x8 matrix format with a bracket/orientation closed Lie algebra. Skew-Hermitian bases for adjacent algebra su(n: 2-8) Lie algebras can be placed in any nxn submatrix position using linear combinations of su(2) Lie algebras. Two distinct representations of su(2) ⨁ su(3) are presented that combine into the direct sum su(2) ⨁ su(3) ⨁ su(3).
Category: Mathematical Physics
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