A 4x4 rank-2 space-time matrix unifying gravity, electromagnetism, strong, and weak interaction by integrating curvature and torsion in geometry

This article deducts that electromagnetic field, strong interaction, and weak interaction are actually torsion tensors. Since we know gravity field is actually a curvature tensor, we can use geometry to unite gravity, electromagnetism, strong, and weak interaction. Perfect fluid combines with Faraday tensor with geometrized unit can give a 4x4 rank2 spacetime matrix to include the above force field. In addition, strong interaction mediating gluons can acquire mass based on Higgs mechanism. This article also provides evidence of Yang-Mills theory existence and solves the mass gap problem in strong interaction.

The Lanczos potential and Chern–Simons theory

In electromagnetism, the Faraday tensor [Formula: see text] can be constructed from the vector potential [Formula: see text], it is possible to add term to the Lagrangian depending on [Formula: see text] but not its derivatives called Chern–Simons terms. In gravitation, the Weyl tensor [Formula: see text] can be constructed from the Lanczos potential [Formula: see text], I pursue the analogy to see if terms of Chern–Simons form can be added to the Lagrangian. A new tensor [Formula: see text] is introduced which is constructed from the Lanczos potential and is of the same form as that of the Weyl tensor [Formula: see text] expressed in terms of the Lanczos potential except that covariant differentiation is replaced by transvection with a vector [Formula: see text]. The new tensor has associated invariants [Formula: see text] and [Formula: see text], the first of these can be interpreted as a Chern–Simons term for Weyl [Formula: see text] gravity. Both invariants allow various tensors to be constructed and some of their properties are investigated by using exact examples.

Eigenvectors of the Faraday tensor of a point charge in arbitrary motion

We study the eigenvalue problem of the Faraday tensor associated with the Liénard–Wiechert electromagnetic field. We find all the eigenvectors (null and nonnull ones) that do not appear explicitly in the literature. PACS Nos.: 03.50De, 02.10Sp, 41.20-q

Physical Consequences of the Interpretation of the Skew Part of gµv in Einstein's Nonsymmetric Unified Field Theory

The electromagnetic interaction in the Einstein-Infeld-Hoffmann (EIH) equations of motion for charged particles in Einstein's unified field theory (EUFT) is found to be automatically precluded by the conventional identification of the skew part of the fundamental tensor with the Faraday tensor. It is shown that an alternative identification, suggested by observations of Einstein, Bergmann and Papapetrou, would lead to the expected electromagnetic interaction, were it not for the intervention of an infelicitous (radiation) gauge. Therefore, an EIH analysis of EUFT is inconclusive as a test of the physical viability of the theory, and it follows that EUFT cannot be considered necessarily unphysical on the basis of such an analysis. Thus, historically, Einstein's unified field theory was rejected for the wrong reason.

Anisotropy of the Faraday effect in non-cubic crystals

The anisotropy of the Faraday effect was studied on 15 optically uniaxial and biaxial crystals by an automated procedure of high resolution. The Faraday tensor of these crystals appears to be not quasi-isotropic. In the vicinity of phase transitions strong anomalies were observed.