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There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
A modification of the Maxwell equations due to the presence of a gravitational field was formerly proposed for a scalar theory with a preferred reference frame. With this modification, the electric charge is not conserved. The aim of the…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
It is shown that in static and spherically symmetric configurations of the system of Maxwell field coupled to 3D gravity with torsion, at least one of the Maxwell field components has to vanish. Restricting our attention to the electric…
It is known that an electric-magnetic duality transformation is a symmetry of the classical source-free Maxwell theory in generic spacetimes. This provides a conserved Noether charge, physically related to the polarization state of the…
The violation of the Noether relation between symmetries and charges is reduced to the time dependence of the charge associated to a conserved current. For the U(1) gauge symmetry a non-perturbative control of the charge commutators is…
The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in presence…
We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over…
In this paper we consider the Einstein-Maxwell theory and define a combined transformation composed of diffeomorphism and $U(1)$ gauge transformation. For generality, we assume that the generator $\chi$ of such transformation is…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving…
On any asymptotically-flat spacetime, we show that the asymptotic symmetries and charges of Maxwell fields on past null infinity can be related to those on future null infinity as recently proposed by Strominger. We extend the covariant…
The classical symmetry of the source-free Maxwell equations under electric-magnetic duality rotations leads to a conserved Noether charge, corresponding to the circular polarization of light. We show that, in quantum field theory, the…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…