相关论文: Revisiting Quaternionic Dual Electrodynamics

By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…

The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of…

In scenarios where electrons are confined to a flat surface, such as graphene, quantizing electrodynamics reveals intriguing insights. We find that one of Maxwell's equations manifests as part of the Hamiltonian, leading to novel…

We work out non-Lorentzian dual actions for electromagnetism and linearised gravity, both in the Carrollian and Galilean cases. This is done in the same way as for Lorentzian theories, by first constructing a parent action that reduces to a…

Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…

Maxwell's equations and the Lorentz force density are expressed using an alternative simultaneity gauge. As a result, they describe electrodynamics for an observer travelling with a constant velocity through an isotropic medium. If desired,…

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic…

After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…

We treat the Christoffel coefficients as operators and introduce new mappings for quaternionic products to connect with the theory of electrodynamics in general spacetime. By utilizing the directional operator of the covariant derivative,…

A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…

Strating with the Maxwell's equations in presence of electric and magnetic sources in an isotropic homogenous medium, we have derived the various quantum equations of dyons in consistent and manifest covariant way. It has been shown that…

We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…

In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…

It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…

We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…

For a monopole, the analogue of the Lorentz equation in matter is shown to be f = g (H - v cross D). Dual-symmetric Maxwell equations, for matter containing hidden magnetic charges in addition to electric ones, are given. They apply as well…

The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are…

The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In…

For D=4 theories of a single U(1) gauge field strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated as an invariance of the actions. The symmetry is associated with duality rotation acting…

It is shown that Euclidean electrodynamics is the exact 4-dimensional analogue of 3-dimensional magnetostatics. This concept is related to a 4-dimensional generalization of the cross product between two vectors where the only essential…