On the Magnetic Current Density in the Maxwell Equations Based on the Noether Theorem

TL;DR

This paper explores the theoretical basis of magnetic current density in Maxwell's equations through Noether's theorem, using quantum gauge fields, symmetry breaking, and string field interactions to relate microscopic currents to macroscopic electromagnetic phenomena.

Contribution

It introduces a novel theoretical framework linking microscopic noncommutative string field interactions to the magnetic current density in Maxwell's equations, based on symmetry breaking and quantum gauge theory.

Findings

Microscopic disjoint current relates to magnetic current density.

Finite resistivities are associated with commutative and noncommutative SFIs.

The framework connects quantum gauge interactions to classical electromagnetic currents.

Abstract

Despite the search for supersymmetry based on abelian and non-abelian Yang-Mills gauge field theory, the Maxwell equations, as the earliest gauge field theory, are non-symmetric because of the undefined term of magnetic current density. This article reports on the theoretical quantization of this term based on spontaneous symmetry breaking in the spatial geometry of a gauge group (G-group) of quantum charged (QC) particles. A locally supersymmetric background-independent spatial geometry of the G-group is developed based on the commutative string field interaction (SFI) between infinite number of QC particles and the grand monopole and the noncommutative SFI of each pair of adjacent QC particles in the G-group. Two adjoint and disjoint currents are associated with the commutative and noncommutative SFIs, respectively, based on the spin of a QC particle. The adjoint and disjoint currents are associated with a zero resistivity between a QC particle and the grand monopole and an infinite resistivity between each pair of adjacent QC particles correlated to their microscopic commutative and noncommutative SFIs in the G-group, respectively. This article demonstrates that the two corresponding resistivities are finite (greater than zero and less than infinity) for the macroscopic commutative and noncommutative SFIs of the G-group. Therefore, the adjoint and disjoint currents are related to the classical macroscopic currents known as electric and magnetic currents, respectively. Because the microscopic adjoint current associated with the commutative SFI has already been related to the macroscopic electric current density in the Maxwell equations, it is proposed that the microscopic disjoint current associated with the noncommutative SFI is related to the undefined magnetic current density in these equations.