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Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, F --> F cos {\theta} + *F sin {\theta}. These transformations are indeed a symmetry of the theory in Noether sense. The…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law.…
We have derived energy conservation equations from the quaternionic Newton's law that is compatible with Lorentz transformation. This Newton's law yields directly the Euler equation and other equations governing the fluid motion. With this…
In a continuum setting, the energy-momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total…
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different…
We present a kind of model of quantum electrodynamics with nonlocal interaction, all the action and the equations of motion of charged particle and electromagnetic field are given. The main characteristics of the theory are: the model obeys…
Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson…
The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…
We reformulate the standard Lagrangian formalism to a reparameterisation invariant Lagrangian formalism by means of Finsler and Kawaguchi geometry. In our formalism, various types of symmetries that appears in theories of physics are…
We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules…
We summarise and discuss some of our previous results, which show that Bohr's theory of the one-electron atom may be derived from the theory underpinning Quantum ElectroDynamics (QED) or vice versa, and that General Relativity may also be…
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of ``improving'' the expressions provided by the…
The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field…
Angular momentum conservation stands as one of the most fundamental and robust laws of physics. In discrete lattices, however, its realization can deviate markedly from the continuous case, especially in the presence of nontrivial…
In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level…
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived.…