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Textbooks play a fundamental role in teaching and learning in school science classrooms. In this paper we investigate the presentation of the nature of the electromagnetic field in a dozen of the world's most popular introductory university…
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.…
Gauge theory is the foundation of the particle physics Standard Model (SM). Considering the multiple gauge sectors for one gauge transformation, we study the generalized Abelian and non-Abelian (Yang-Mills theory) gauge theories. We first…
Main properties of noncommutative (NC) gauge theory are investigated in a $2-$dimensional twisted Moyal plane, generated by vector fields $X_{a}=e_{a}^{\mu}(x)\partial_{\mu};$ the dynamical effects are induced by a non trivial tensor…
Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological…
We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons…
The new nonlinear axionically extended version of the general relativistic magnetohydrodynamics is formulated. The self-consistent formalism of this theory is based on the introduction into the Lagrangian of the new unified scalar…
Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex,…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any…
Bekenstein and Mayo proposed a generalised bound for the entropy, which implies some inequalities between the charge, energy, angular momentum, and the size of the macroscopic system. Dain has shown that Maxwell's electrodynamics satisfies…
We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even,…
In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…
We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our…
We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…
In this paper, we describe non-abelian gauge bundles with magnetic and electric fluxes on higher dimensional noncommutative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft fluxes. We discuss…